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Welcome to the Math Salamanders 2d Shapes Worksheets. We have a wide selection of worksheets on 2d shapes, including symmetry worksheets, naming 2d shapes, shape riddles and puzzles, and sheets about the properties of 2d shapes. There are a range of worksheets at different levels, suitable for children from Kindergarten and up.

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2d Shape Worksheets

There are a range of geometry worksheets set out in different sections as follows:

Kindergarten Section

  • identify 2d shapes from pictures
  • tracing and shading 2d shapes

1st Grade Section

  • sorting 2d and 3d shapes
  • identify different types of 2d shapes.
  • drawing shapes using positional language - inside, above, below,...

2nd Grade Section

  • identify and name members of the triangle family, e.g. equilateral triangles.
  • identifying and sorting other 2d shapes
  • identify simple properties of 2d shapes - sides, corners, right angles
  • solving riddles involving 2d shapes

3rd Grade Section

  • identifying a range of 2d shapes;
  • knowing and using properties of 2d shapes - sides, symmetry, right angles
  • investigate properties and features of 2d shapes
  • symmetry worksheets
  • 2d shapes worksheets - area and perimeter

4th Grade Section

  • classify and measure a range of angles
  • using coordinates in the 1st quadrant

5th Grade Section

  • knowing properties of angles of triangles and quadrilaterals
  • finding missing angles
  • area of triangles and quadrilaterals

Geometry Riddles

  • Reasoning and exploring the properties of 2d shapes.

2D Shape Clipart

  • A range of printable clipart for 2d shapes.

Parts of a Circle Worksheets & Support

  • Worksheets and support for finding and naming the parts of a circle.

Identify 2D Shapes Online Quiz

  • an online quiz to help develop naming and identifying a range of 2D shapes.

Kindergarten 2d Shapes Worksheets

  • Shade the Circles Sheet 1
  • Shade the Rectangles Sheet 1
  • Shade the Squares Sheet 1
  • Count the Shapes 1
  • Match the Shapes Sheet 1
  • Trace the Shape Sheet 1
  • Trace the Shape Sheet 1a
  • Trace the Shape Sheet 2
  • Trace the Shape Sheet 2a

More Kindergarten Geometry Resources

  • More Kindergarten Shape Worksheets
  • More Kindergarten Tracing Worksheets
  • Top of Page

1st Grade Shape Worksheets

  • Identify Squares and Rectangles 1
  • Identify Squares and Rectangles 1 Answers
  • Identify Triangles and Circles
  • Identify Triangles and Circles Answers
  • Identify Simple 2d Shapes 1
  • Identify Simple 2d Shapes 1 Answers
  • Draw 2d Shapes 1

More 1st Grade Geometry Resources

  • More 1st Grade Geometry Worksheets

2nd Grade Shape Worksheets

  • Identify Triangles 1
  • Identify Triangles 1 Answers
  • Identify Triangles 2
  • Identify Triangles 2 Answers
  • Identify 2d Shapes 1
  • Sheet 1 Answers
  • Identify 2d Shapes 2
  • Sheet 2 Answers
  • Block Symmetry Sheet 1
  • Name and Trace 1
  • Name and Trace 2
  • Name and Trace 3
  • Name and Trace 3 (UK version)
  • Name and Trace 4
  • Name and Trace 4 (UK version)

More 2nd Grade Geometry Resources

  • More Second Grade Geometry Worksheets
  • More Block Symmetry Worksheets

3rd Grade Shape Worksheets

  • 2d Shapes Properties 1
  • 2d Shapes Properties 2
  • 2d Shapes - Can you draw it 1
  • Can you draw it 1 Answers
  • The Alphabet in Symmetry
  • The Alphabet in Symmetry Answers
  • Block Symmetry Sheet 5
  • Sheet 5 Answers
  • Line Symmetry 1
  • Area Sheet 1

More 3rd Grade Geometry Resources

  • More 3rd Grade Geometry Worksheets
  • More Line Symmetry Worksheets

4th Grade Shapes Worksheets

  • Angle Classification 1
  • Angle Classification 2
  • Triangle Classification 1
  • Angle Measuring 1
  • Angle Measuring 2
  • Plot the Coordinates Sheet 1
  • Area Sheet 4
  • Sheet 4 Answers

More 4th Grade Geometry Resources

  • More 4th Grade Geometry Worksheets
  • More Coordinate Worksheets
  • More Area Worksheets

5th Grade Shapes Worksheets

  • Angles to 90°
  • Angles to 90° Answers
  • Angles on a straight line
  • Angles on a straight line Answers
  • Angles around a point 1
  • Angles around a point 1 Answers
  • Angles in a triangle 1
  • Angles in a triangle 1 Answers
  • Find the missing angle 1
  • Find the missing angle 1 Answers

More 5th Grade Geometry Resources

  • More 5th Grade Geometry Worksheets
  • Explore 2d Shapes Worksheets

Looking for some geometry worksheets to get children thinking and reasoning about 2d shapes?

The shapes on this page are all about children really understanding what 2d shapes are all about, and using their reasoning skills to justify their thinking.

Using these sheets will help your child to:

  • know the properties of a range of 2d shapes;
  • recognise that some shapes can also be described as being other shapes; e.g. a square is also a rhombus;
  • recognise and understand right angles, parallel lines, lines of symmetry;
  • develop their geometric reasoning skills.

Here you will find our free printable geometry riddles from 1st to 5th grade.

These riddles are all about problem solving with 2d shapes.

Using these riddles will help your child to:

  • develop their geometry skills;
  • develop their understanding of geometric language;
  • apply their geometric knowledge to solve problems.

All the geometry riddles in this section support elementary math benchmarks.

  • Geometry Worksheets (Riddles)

Here you will find a selection of 2D shape sheets designed to help your child learn their names and properties of 2d shapes.

  • recognise a range of 2D shapes;
  • recognise that a square is also a member of the rectangle family;
  • recognise shapes in different orientations and sizes.

All the free printable shape sheets in this section support Elementary Math benchmarks.

  • Shapes Clipart - Basic 2D Shapes
  • Shapes Clip art - Triangle and Quadrilateral Families
  • Shapes for Kids - Regular Polygons (individual)
  • Regular Shapes (groups)
  • Printable Shapes - 2D and 3D Shape Sheets

Parts of a Circle Worksheets and Support

Do you know the special geometric names to describe the different parts of a circle?

Well you can find all the support you need on this page, complete with some practice worksheets and an online quiz!

  • Parts of a Circle Worksheets

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This quick quiz tests your knowledge and skill at indentifying 2D shapes including types of triangle..

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Size worksheets for kinder - Pre-K Free Size comparison printable - Area model multiplication examples and test

  • 3rd Grade Math Worksheets

Free printable 3rd Grade 2D shapes worksheets for math practice

Welcome to this amazing world of teaching 3 rd graders about 2D shapes. In this article, we will provide you with everything you need to know about 2D shapes for 3rd grade, including what they are, how to identify them, and how to compare and classify them. However, we encourage you to visit Mathskills4kids.com and find a variety of free printable 3rd Grade 2D shapes worksheets for extra math practice at home and in the classroom.

Are you looking for a fun and easy way to help your 3rd graders learn about 2D shapes ? Do you want to boost their math skills and confidence with engaging and interactive activities? If you answered yes to these questions, you are in the right place!

Download and use our worksheets right away!

Let’s get started!

Why 2D shapes matter for 3rd Graders

There are so many reasons why 2D shapes matter to 3 rd graders . First, they are everywhere in our world. They are the building blocks of many objects, patterns, designs, and art. Learning about 2D shapes helps 3rd graders develop spatial awareness, geometry, measurement, and problem-solving skills.

It also prepares them for more advanced math topics in the future, such as area, perimeter, fractions, and algebra.

An amazing unique thing about these Mathskills4kids’ 3 rd Grade 2D shapes worksheets is that they cover various 2D shapes concepts that, by the end of 3rd grade, students will be able to:

  • Recognize and name common 2D shapes such as circles, squares, rectangles, triangles, pentagons, hexagons, octagons, etc.
  • Describe the properties of 2D shapes such as sides, vertices (corners), angles, parallel and perpendicular lines, symmetry, etc.
  • Compare and classify 2D shapes based on their properties and attributes .
  • Identify and draw lines of symmetry in 2D shapes .
  • Identify congruent (same size and shape) and similar (same shape but different size) 2D shapes .
  • Identify and perform transformations such as reflection (flip), rotation (turn), and translation (slide) on 2D shapes.
  • Apply 2D shapes knowledge to real-life situations and problems .

BROWSE THE WEBSITE

Download free worksheets, 3rd grade math topics.

  • Number and compapring
  • Place value

Subtraction

  • Understand multiplication
  • Multiplication skill builders
  • Multiplication fluency

Multiplication

  • Understand division
  • Division skill builders
  • Division fluency
  • Division practice
  • Mixed operation
  • Equations & variations
  • Estimate & rounding
  • Logical reasoning
  • Telling time
  • Data graph & probability
  • Understanding fractions
  • Equivalent fractions
  • Comparing and ordering fractions
  • Operations with fractions
  • Unit of measurement
  • Two-dimensional shapes
  • Triangles and quadrilaterals
  • Geometric measurement

Free printable 3rd Grade 2D shapes worksheets for math practice - Counting sides and vertices in two-dimensional shapes

Start practice on Third Grade here

What are 2d shapes, and how to identify them.

A 2D shape is flat with only two dimensions: length and width. It does not have any thickness or depth. You can draw a 2D shape on paper or a screen.

To identify a 2D shape , you need to look at its features, such as:

  • The number of sides it has . A side is a straight or curved line that forms the edge of a shape.
  • The number of vertices it has . A vertex (plural: vertices) is a point where two or more sides meet. It is also called a corner.
  • The type and size of angles it has . An angle is the amount of turn between two sides. There are three types of angles : acute (less than 90 degrees), right (exactly 90 degrees), and obtuse (more than 90 degrees).
  • The length of its sides . Some shapes have equal sides (all the same length), while others have unequal sides (different lengths).
  • The relationship between its sides . Some shapes have parallel sides (always the same distance apart), while others have perpendicular sides (meet at right angles). Some shapes have both parallel and perpendicular sides.

Types of 2D Shapes and their Properties

There are many types of 2D shapes , but here are some of the most common ones that you will encounter in our free printable 3rd Grade 2D shapes worksheets math practice :

  • Circle : A circle is round with no sides or vertices. It has one curved line that is always the same distance from the center. The distance from the center to any point on the circle is called the radius. The distance across the circle through the center is called the diameter. The distance around the circle is called the circumference.
  • Square : A square is a four-sided shape with four equal sides and four right angles. It has four vertices. A square is a special type of rectangle that has all equal sides.
  • Rectangle : A rectangle is a four-sided shape with two pairs of equal sides and four right angles. It has four vertices. A rectangle can be a square if all its sides are equal.
  • Triangle : A triangle is a three-sided shape with three vertices and angles. The sum of the angles in any triangle is always 180 degrees. There are different types of triangles based on their sides and angles:
  • Equilateral triangle : A triangle with three equal sides and three equal angles (60 degrees each).
  • Isosceles triangle : A triangle with two equal sides and two equal angles opposite them.
  • Scalene triangle : A triangle that has no equal sides or angles.
  • Right triangle : A triangle with one right angle and two acute angles.
  • Acute triangle : A triangle that has three acute angles.
  • Obtuse triangle : A triangle with one obtuse angle and two acute angles.
  • Pentagon : A pentagon is a five-sided shape with five vertices and five angles. The sum of the angles in any pentagon is always 540 degrees. There are different types of pentagons based on their sides and angles:
  • Regular pentagon : A pentagon has five equal sides and five equal angles (108 degrees each).
  • Irregular pentagon : A pentagon that has no equal sides or angles.
  • Hexagon : A hexagon is a six-sided shape with six vertices and six angles. The sum of the angles in any hexagon is always 720 degrees. There are different types of hexagons based on their sides and angles:
  • Regular hexagon : A hexagon has six equal sides and six equal angles (120 degrees each).
  • Irregular hexagon : A hexagon that has no equal sides or angles.
  • Octagon : An octagon is an eight-sided shape with eight vertices and eight angles. The sum of the angles in any octagon is always 1080 degrees. There are different types of octagons based on their sides and angles:
  • Regular octagon : An octagon with eight equal sides and eight equal angles (135 degrees each).
  • Irregular octagon : An octagon that has no equal sides or angles.

How to compare and classify 2D shapes

To compare 2D shapes , look at their properties and their similarities or differences. For example, you can compare two shapes by their number of sides, vertices, type, size of angles, length of sides, relationship between sides, etc.

To classify 2D shapes , you need to group them into categories based on their properties. For example, you can classify shapes by their number of sides (quadrilaterals, pentagons, hexagons, etc.), by their type of angles (right, acute, obtuse, etc.), by their symmetry (symmetrical, asymmetrical), etc.

Fun activities to practice 2D shapes skills

Learning about 2D shapes can be fun and engaging with these activities:

  • Shape Hunt : Go on a shape hunt around your house or neighborhood and find as many 2D shapes as possible. Take pictures or draw them in a notebook. Label each shape with its name and properties.
  • Shape Art : Use different 2D shapes to create your artwork. You can cut out shapes from paper or cardboard or use stickers, stamps, or magnets. Arrange the shapes into patterns, designs, or pictures. You can also use shapes to make letters, numbers, or words.
  • Shape Puzzles : Cut out different 2D shapes from paper or cardboard and mix them up. Then try to put them back together to form larger shapes. To make shape puzzles, you can also use tangrams, pattern blocks, or geoboards.
  • Shape Bingo : Make your bingo cards with different 2D shapes on them. Then call out the names of the shapes and mark them on your card. The first one to get a row, column, or diagonal wins!
  • Shape Memory : Make pairs of cards with matching 2D shapes. Shuffle the cards and place them face down on a table. Take turns flipping over two cards at a time and try to find the matching pairs. If you find a pair, keep it and go again. If not, turn them back over and let the next player try. The one with the most pairs at the end wins!

Our selection of Mathskills4kids’ free printable 3 rd Grade 2D shapes worksheets for math practice

We have selected a variety of free printable 3 rd -grade 2D shapes worksheets from Mathskills4kids.com that will help your 3 rd graders practice their 2D shapes skills in a fun and engaging way. These worksheets cover different topics related to 2D shapes, such as:

  • Identify two-dimensional shapes : In this worksheet, students will name the 2D shapes shown in the pictures. They can choose from a word bank that includes a circle, square, rectangle, triangle, pentagon, hexagon, octagon, trapezoid, parallelogram, and rhombus.
  • Counting sides and vertices in 2-dimensional shapes : In this worksheet, students will count how many sides and vertices each 2D shape has and write the numbers in the boxes. They can use the shape names as a hint.
  • Identify open and closed shapes : In this worksheet, students will identify which shapes are open and closed. They have to color the open shapes red and the closed shapes blue.
  • Identifying a polygon : In this worksheet, students will identify which shapes are polygons and which are not. They have to color the polygons green and the non-polygons yellow.
  • Identifying points, lines, line segments, and rays : In this worksheet, students will identify what kind of geometric element is shown in each picture. They have to write P for point, L for line, LS for line segment, or R for ray.
  • Identifying angles greater than, less than, or equal to a right angle : In this worksheet, students will identify the angle type shown in each picture. They have to write > for greater than a right angle, < for less than a right angle, or = for equal to a right angle.
  • Parallel, perpendicular, and intersecting lines : In this worksheet, students will identify the relationship between the pairs of lines shown in each picture. They will write P for parallel, PE for perpendicular, or I for intersecting.
  • Reflection, rotation, and translation : In this worksheet, students will identify what transformation has been applied to each shape. They will write R for reflection, RO for rotation, or T for translation.
  • How to identify congruent shapes : In this worksheet, students will identify which pairs of shapes are congruent and which are not. They have to color the congruent pairs green and the non-congruent pairs orange.
  • Symmetry : In this worksheet, students will identify symmetrical shapes from asymmetrical ones. They have to draw a line of symmetry on each symmetrical shape and color it purple.

How to use 2D shapes worksheets effectively to boost 3rd graders’ math skills

These worksheets are designed to help third graders practice their 2D shapes skills in a fun and engaging way. However, they are not meant to replace direct instruction or hands-on activities. Here are some tips on how to use 2D shapes worksheets effectively to boost 3rd graders’ math skills :

  • Before giving the worksheets to your students, review the concepts and vocabulary related to 2D shapes with them. You can use flashcards, posters, or interactive games to reinforce learning.
  • Explain the instructions clearly and model how to complete each type of worksheet. You can use a projector or a smart board to show examples and demonstrate how to solve the problems.
  • Provide feedback and guidance as your students work on the worksheets. You can check their answers with an answer key or use self-checking worksheets with QR codes or hidden messages.
  • Encourage your students to use different strategies and tools to solve the problems. You can provide them with manipulatives such as geoboards or pattern blocks or let them use online tools such as virtual manipulatives or geometry apps.
  • Differentiate the worksheets according to your student’s needs and abilities. You can modify the difficulty level, the number of problems, the type of questions, or the worksheet format to suit your student’s learning styles and preferences.
  • Extend the learning beyond the worksheets by asking your students to apply their 2D shapes skills in real-life scenarios. You can ask them to find examples of 2D shapes in their environment, create them using different materials or design their worksheets for their peers.

Applying 2D shapes in real-life scenarios

One of the best ways to help your students understand and appreciate 2D shapes is to show them how they are used in real-life scenarios. Here are some examples of how you can connect 2D shapes to different subjects and topics:

  • Art : You can ask your students to create artwork using different 2D shapes. You can inspire them with examples of famous artists who used geometric shapes in their paintings, such as Piet Mondrian, Wassily Kandinsky, or Paul Klee. You can also challenge them to create optical illusions or tessellations using 2D shapes.
  • Science : You can ask your students to explore the properties and characteristics of 2D shapes with science concepts . For example, you can ask them to investigate how light reflects and refracts on different 2D shapes , how sound waves travel through different 2D shapes, or how forces affect the stability and strength of different 2D shapes .
  • Social Studies : You can ask your students to identify and compare the 2D shapes used in different cultures and civilizations. For example, you can ask them to research how ancient Egyptians used 2D shapes in their architecture, art, and writing, how Native Americans used 2D shapes in their symbols and patterns, or how the Chinese used 2D shapes in their paper cutting and lantern making.
  • Language Arts : You can ask your students to use 2D shapes as a creative writing prompt. For example, you can ask them to write a story based on a shape they draw or choose, a poem using shape words, or a riddle describing a shape without naming it.

Bonus: Find more resources to reinforce 2D shapes learning in Third Grade here!

If you are looking for more resources to reinforce 2D shapes learning in third grade , you are in luck! We have compiled a list of some of the best online resources that offer free games, videos, quizzes, and activities related to 2D shapes.

Here are some of our favorites:

  • Math is Fun : This website has a lot of information and examples about 2D shapes, their properties, and how to classify them. You can also find interactive tools to explore shapes and measure angles. https://www.mathsisfun.com/geometry/plane-geometry.html
  • Khan Academy : This online platform has a series of videos and exercises that cover 2D shapes and other geometry topics. You can watch the videos to learn new concepts, practice what you learned with quizzes, and track your progress. https://www.khanacademy.org/math/cc-third-grade-math/imp-geometry
  • com : This website has a variety of games and worksheets that you can use to practice 2D shapes in a fun way. You can play matching games, puzzles, bingo, and more. You can also print out worksheets to color, cut, and glue shapes. https://www.education.com/resources/third-grade/geometry/

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Conclusion: Keep Practicing and Have Fun

We hope you enjoyed this article about free printable 3 rd -grade 2D shapes worksheets for math practice . We hope these worksheets will help your students improve their 2D shapes skills and have fun along the way.

Remember to check out our other articles and website, Mathskills4kids.com , for more free printable worksheets for third graders on different math topics. Happy learning!

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Properties of Shapes KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

problem solving 2d shape

Seeing Squares

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

problem solving 2d shape

Triple Cubes

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

problem solving 2d shape

Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

problem solving 2d shape

Sorting Logic Blocks

This activity focuses on similarities and differences between shapes.

problem solving 2d shape

The Third Dimension

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

problem solving 2d shape

Building Blocks

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

problem solving 2d shape

Counters in the Middle

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

problem solving 2d shape

Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

problem solving 2d shape

National Flags

This problem explores the shapes and symmetries in some national flags.

problem solving 2d shape

Round a Hexagon

This problem shows that the external angles of an irregular hexagon add to a circle.

problem solving 2d shape

Nine-pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

problem solving 2d shape

Let Us Reflect

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

problem solving 2d shape

Name That Triangle!

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

problem solving 2d shape

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

problem solving 2d shape

Guess What?

Can you find out which 3D shape your partner has chosen before they work out your shape?

problem solving 2d shape

The Numbers Give the Design

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

problem solving 2d shape

Where Are They?

Use the isometric grid paper to find the different polygons.

problem solving 2d shape

Seeing Parallelograms

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

problem solving 2d shape

A Puzzling Cube

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

problem solving 2d shape

Use the information on these cards to draw the shape that is being described.

problem solving 2d shape

How Safe Are You?

How much do you have to turn these dials by in order to unlock the safes?

problem solving 2d shape

Square Corners

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

problem solving 2d shape

Six Places to Visit

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

problem solving 2d shape

Overlapping Again

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

problem solving 2d shape

Egyptian Rope

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Shapes on the Playground

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

problem solving 2d shape

A task which depends on members of the group noticing the needs of others and responding.

problem solving 2d shape

Stringy Quads

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

problem solving 2d shape

Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

problem solving 2d shape

Sponge Sections

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

problem solving 2d shape

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

problem solving 2d shape

Seeing Rhombuses

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

problem solving 2d shape

Arranging Cubes

A task which depends on members of the group working collaboratively to reach a single goal.

problem solving 2d shape

Move Those Halves

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

problem solving 2d shape

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Quadrilaterals

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

problem solving 2d shape

Triangles All Around

Can you find all the different triangles on these peg boards, and find their angles?

problem solving 2d shape

Reflector ! Rotcelfer

Can you place the blocks so that you see the reflection in the picture?

problem solving 2d shape

Olympic Turns

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

problem solving 2d shape

Board Block Challenge

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

problem solving 2d shape

Symmetry Challenge

How many symmetric designs can you make on this grid? Can you find them all?

problem solving 2d shape

Making Spirals

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

problem solving 2d shape

Stick Images

This task requires learners to explain and help others, asking and answering questions.

problem solving 2d shape

Estimating Angles

How good are you at estimating angles?

problem solving 2d shape

What Shape?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

problem solving 2d shape

Making Rectangles

problem solving 2d shape

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

problem solving 2d shape

What can you see? What do you notice? What questions can you ask?

problem solving 2d shape

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Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

GCSE Maths

Here we will learn about 2D shapes, including symmetry, perimeter, area, circles, sectors, arcs and angles in polygons.

There are also 2D shapes worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are 2D shapes?

2D shapes are flat shapes which only have two dimensions; length and width.

Some examples of common 2D shapes names are triangles, rectangles, pentagons, hexagons, heptagons, octagons, nonagons, decagons and circles.

2D shapes image 1

We can solve problems involving 2D shapes using a variety of methods.

What are 2D shapes?

Polygons are 2D shapes made from straight lines. You will deal with two different types of polygons.

Regular polygons

Regular polygons have specific properties. They have all sides of equal length and all interior angles are equal.

Examples of basic 2D shapes that are regular polygons are equilateral triangles and squares.

Irregular polygons

Irregular shapes (or polygons) do not have all equal sides and do not have all equal angles . When the number of sides is unknown, we describe this shape as an \textbf{n-gon} where the number of sides is given as \textbf{n}.

You will also need to be able to solve problems involving angles in polygons. The angles in a polygon can help determine whether a polygon is regular, a specific type of polygon or to determine how many sides a polygon has. You need to be familiar with interior and exterior angles of polygons.

Interior angles are angles that are contained within the polygon.

2D shapes image 2

The sum of interior angles of any polygon can be calculated using the formula,

Sum of interior angles = (n-2) \times 180

where n represents the number of sides.

Exterior angles are supplementary to the interior angle. This means that the sum of the interior and exterior angles at a vertex always equals 180^{o}. We can use this property to find either the interior angle, or exterior angle at a vertex.

For any polygon the sum of exterior angles of a polygon 360^{o}.

2D shapes image 3

Step-by-step guide: Polygons

Symmetry is when a line is drawn through a shape to make one side of the line a reflection of the other. It is a property of a 2D polygon or 3D polyhedron.

There are two different types of symmetry that you need to be aware of. Lines of symmetry and rotational symmetry .

For example, a rectangle has two lines of symmetry

2D shapes symmetry image 1

and has order 2 rotational symmetry.

2D shapes symmetry image 2

Step-by-step guide: Symmetry

Area is a measure of how much space there is inside of a 2 dimensional shape.

Here are formulae we need to remember to calculate the area of certain 2D shapes.

These are seen in the table below.

2D shapes area image 1

Step-by-step guide: How to work out area

The perimeter is the total distance around the outside of a 2D shape.

For example, let’s find the perimeter of the triangle.

2D shapes perimeter image 1

For example, let’s find the perimeter of the rectangle.

The opposite sides of a rectangle are equal, a and b are the side lengths.

2D shapes perimeter image 2

For example, let’s find the perimeter of the circle.

The perimeter of a circle is known as the circumference of a circle.

2D shapes perimeter image 3

The circumference of this circle is

Step-by-step guide: How to work out perimeter

  • Circles, sectors and arcs

Circles are round plane figures whose boundaries consist of points equidistant from a fixed point (the centre of the circle).

2D shapes circles, sectors and arcs image 1

As well as the area and circumference of a circle we can also work out the following.

Step-by-step guide: Circles, sectors and arcs

  • Parts of a circle

The parts of a circle have specific names and properties which you need to know for all circle related questions. An important fact to remember is that the radius of a circle is half of its diameter.

2D shapes circles, sectors and arcs image 2

Step-by-step guide: Parts of a circle

  • Area of a sector

The area of a sector is part of the area of a circle.

It can be found by using the formula \frac{\theta}{360} \times \pi r^{2}.

2D shapes circles, sectors and arcs image 3

For example,

2D shapes circles, sectors and arcs image 4

The area of this sector is

Step-by-step guide: Area of a sector

See also: Sector of a circle

The arc of a circle is part of the circle’s circumference.

It’s length can be found using the formula \frac{\theta}{360} \times \pi d.

2D shapes circles, sectors and arcs image 5

The arc length of this sector is

Step-by-step guide: Arc length

See also: Arc of a circle

  • Perimeter of a sector

To find the perimeter of a sector you need to find the arc length and then add it to the two straight sides which are both radii (i.e. the length around the outside of the sector).

2D shapes circles, sectors and arcs image 7

The perimeter of this sector is

Step-by-step guide: Perimeter of a sector

  • Segment of a circle

A segment of a circle is created by an arc length and a chord.

You may have to find its area using a combination of mathematical rules such as trigonometry or Pythagoras’ theorem.

2D shapes circles, sectors and arcs image 9

Step-by-step guide: Segment of a circle

  • Equation of a circle

The equation of a circle (at GCSE) can be given in the form below

2D shapes circles, sectors and arcs image 10

Step-by-step guide: Equation of a circle

How to use 2D shapes

We can use 2D shapes in lots of different ways.

We will learn about:

Explain how to use 2D shapes

Explain how to use 2D shapes

Area of 2D shapes worksheet

Get your free 2D shapes worksheet of 20+ area of 2D shapes questions and answers. Includes reasoning and applied questions.

2D shapes examples

Example 1: regular / irregular polygons.

The shape ABCDE below is made from two scalene triangles, and one isosceles triangle. M is a midpoint on the line CD . AM is a line of symmetry.

2D shapes example 1 image 1

Determine what type of polygon ABCDE is and determine if it is regular or irregular.

  • State / calculate the number of sides of the polygon.

The polygon ABCDE has 5 sides so it is a type of pentagon.

2 Determine the size of the angles / side lengths within the polygon.

As triangle ACD is isosceles and AM is a line of symmetry, angle ACD = angle ADC = 52^{o}.

As the sum of angles in a triangle is 180^{o},

angle CAD = 180-(52+52)=76^{o}.

As AM is a line of symmetry, triangles ABC and ACD must be congruent, sharing the same angles and side lengths. This means that,

  • Angle BCA = angle ADE =56^{o}
  • Angle DAE = angle CAB =16^{o}

Again, as the sum of angles in a triangle total 180^{o},

angle AED = 180-(56+16)=108^{o}.

This is the same for angle ABC as it is symmetrical to angle AED and therefore equal.

We now have all of the following angles,

2D shapes example 1 image 2

3 Recognise the other properties of the polygon.

For a pentagon to be regular, all of the interior angles must be the same and side lengths must be the same.

Furthermore, as the interior angle sum of a pentagon is 540^{o}, each interior angle of a regular pentagon is equal to

Adding the angles at each vertex together, we have

2D shapes example 1 image 3

Each interior angle of the polygon ABCDE is equal to 108^{o}.

However, the triangles AED and ABC are scalene. Therefore, AB has a different length to BC .

The interior angles are equal but the side lengths are not equal.

The polygon is an irregular pentagon.

Example 2: types of quadrilateral

Determine what type of quadrilateral ABCD is below.

2D shapes example 2 image 1

Determine the size of the angles / side lengths within the quadrilateral.

All four side lengths are equal to 9cm with two pairs of parallel sides.

Angle BCD = 48+48=96^o and so ABCD cannot be a square.

CDE is a triangle. As the sum of angles in a triangle total 180^{o},

angle CED = 180-(42+48)=90^{o}.

Labelling this on the diagram, we have

2D shapes example 2 image 2

Recognise the other properties of the polygon.

As vertically opposite angles are equal, angle AED = angle CED = 90^{o}.

As the sum of angles on a straight line total 180^{o},

Angle AED = 180-90=90^{o}.

This is also true for angle BEC .

We therefore have the diagonals intersecting at 90 degrees.

2D shapes example 2 image 3

ABCD is a rhombus.

Remember: The properties of a rhombus are,

  • Four equal sides
  • Opposing sides are parallel
  • Two opposing pairs of equal angles
  • Diagonals bisect each other at 90 degrees
  • Two lines of symmetry
  • Rotational symmetry of order 2

Example 3: symmetry

State the number of lines of symmetry for a regular hexagon.

2D shapes example 3 image 1

Locate the centre of the 2D shape.

To locate the centre of a shape with an even number of vertices, draw a pair of straight lines connecting two opposing vertices.

2D shapes example 3 image 2

Use a ruler to visualise a horizontal and/or vertical line of symmetry through the centre of the shape.

The regular hexagon has a vertical line of symmetry.

problem solving 2d shape

The regular hexagon has a horizontal line of symmetry.

2D shapes example 3 image 4

Continue to rotate the ruler around 180 degrees over the centre point to cover all sides and vertices.

Line of symmetry 3.

2D shapes example 3 image 5

Line of symmetry 4.

2D shapes example 3 image 6

Line of symmetry 5.

2D shapes example 3 image 7

Line of symmetry 6.

2D shapes example 3 image 8

A regular hexagon has 6 lines of symmetry.

2D shapes example 3 image 9

Example 4: area of an isosceles triangle

Calculate the area of the triangle below.

2D shapes example 4 image 1

Identify the base and perpendicular height of the triangle.

The two values that are perpendicular to one another are the 12cm along the base, and the vertical height of 8cm.

The 10cm is not required to find the area of this triangle.

Write the area formula.

The area of a triangle formula is,

\text{Area of a triangle}=\cfrac{\text{base }\times\text{height}}{2}.

Substitute known values into the area formula.

As the base = 12cm and the height = 8cm, we have

\text{Area of a triangle }=\cfrac{12\times{8}}{2}.

Solve the equation.

Write the answer, including the units.

As the units of length are in centimetres, the units of area are square centimetres.

The area of the triangle is 48cm^{2}.

Example 5: circumference of a circle

Calculate the circumference of a circle with a radius of 4cm. Write your answer correct to 2 decimal places.

2D shapes example 5 image 1

Find the radius or diameter of the circle.

The radius of the circle is 4cm.

Use the relevant formula to calculate the circumference of the circle.

The formula for the circumference of a circle (C) in terms of the radius (r) is

Substituting r=4 into the formula, we have

\begin{aligned} C&=2\times\pi\times{4} \\\\ &=8\times\pi \\\\ &=8\pi \\\\ &=25.13274123 \\\\ &=25.13\text{ (2dp)} \end{aligned}

Give your answer clearly with the correct units.

The circumference of the circle is 25.13cm \ (2dp).

Example 6: perimeter of compound shapes – real life problem

A car park needs a new boundary fence installing. A sketch of the car park is given below.

2D shapes example 6 image 1

Determine the length of the boundary wall (the car park entrance/exit must not be included in this value).

Add all the side lengths.

A few of the side lengths are missing and so we need to calculate these lengths first.

As AF = 8.8m and DE = 2.9m, the length of BC can be calculated by subtracting DE from AF ,

8.8-2.9 = 5.9m.

As AB = 12.4m and CD = 3.5m, the length of EF can be calculated by adding AB and CD together,

12.4+3.5=15.9m.

Writing these two measurements onto the diagram, we have

2D shapes example 6 image 2

The perimeter is the sum of the side lengths and so we have the sum,

12.4+5.9+3.5+2.9+15.9+8.8=49.4m.

Note: For an L shape, this is the same as doubling the sum of the height and the width ((8.8+15.9)\times{2}=49.4m).

Write the final answer with the correct units.

As we need to calculate the boundary excluding the entrance/exit, we need to subtract the width of the entrance from the total perimeter.

49.4-2.4=47m

The perimeter of the car park excluding the entrance/exit is 47m.

Example 7: area of a sector

A circular cake is cut into 8 equal slices as shown below.

2D shapes example 7 image 1

Calculate the area of the top of one slice of cake.

Find the length of the radius \textbf{r} .

The radius r = 9.5cm.

Find the size of the angle creating the sector

The angle of the sector is one eighth of a full turn. As a full turn is 360 degrees,

360\div{8}=45.

The angle of the sector is 45^{o}.

Substitute the value of the radius and the angle into the formula for the area of a sector.

The formula for the area of the sector is

\text{Area of a sector }=\frac{\theta}{360}\times\pi{r}^{2}

where \theta is the angle of the sector, and r is the radius of the overall circle.

Substituting \theta=45^{o} and r = 9.5cm, we have

\begin{aligned} \text{Area of a sector }&=\frac{45}{360}\times\pi\times{9.5}^{2} \\\\ &=\frac{1}{8}\times\pi\times{90.25} \\\\ &=11.28125\pi \\\\ &=35.44109212 \\\\ &=35.44\text{cm}^{2}\text{ (2dp)} \end{aligned}

Clearly state your answer.

The area of the top of the cake slice is 35.44cm^{2}.

Example 8: equation of a circle

Determine the equation of the unit circle, centred at the origin.

2D shapes example 8 image 1

Write the general equation of a circle.

The general equation of a circle is x^{2}+y^{2}=r^{2}.

State any variables you know.

The radius of the unit circle is 1. We can also see this as the centre of the circle lies at the point (0,0) and a coordinate on the circumference of the circle is (1,0), giving us a radius of 1.

Substitute any values you know into the equation.

Substituting r=1 into the equation of a circle, we have

x^{2}+y^{2}=1^{2}.

Use the information you have to solve the problem.

Evaluating 1^{2} we get 1^{2}=1 \times 1=1.

Clearly state the answer.

The equation of the unit circle, centred at the origin is x^{2}+y^{2}=1.

Common misconceptions

  • Rotational symmetry/lines of symmetry

Lines of symmetry are often confused with rotational symmetry. A line of symmetry on a two-dimensional shape divides the shape equally into two symmetrical pieces. Rotational symmetry is the number of times a shape fits into itself when rotated around its centre.

  • Confusing perimeter with area

Remember, perimeter is distance around the outside of a shape, whilst area is the space inside the shape.

  • Angles properties

Ensure you have a good understanding of the different types of angles (for example, acute angles and right angles) along with how to calculate angles in polygons and angles in parallel lines. Getting these confused can lead to misconceptions when problem solving.

Practice 2D shapes questions

1. Which of the following shapes has 2 lines of symmetry and rotational symmetry order 2.

Parallelogram

GCSE Quiz False

A parallelogram has no lines of symmetry and rotational symmetry order 2.

A square has 4 lines of symmetry and rotational symmetry order 4.

A kite has 1 line of symmetry and no rotational symmetry.

2D shapes practice question 1

2. The rectangle has a perimeter of 42cm. Find x.

2D shapes practice question 2

Form an equation for the perimeter.

Solve the equation, to find x=4.

3. Find the area of the isosceles triangle.

2D shapes practice question 3

This is an isosceles triangle. We can split it vertically to form two identical triangles with base 6cm, and hypotenuse 10cm.

We then use Pythagoras’ theorem to find the height of the triangle.

Then we can use the formulae for the area of a triangle, and multiply the height by the base (remembering to use the base as 12cm for the area of the whole triangle) then divide by 2.

4. The sector has an area of \frac{27}{2} \pi cm^2, Find the perimeter in terms of \pi.

2D shapes practice question 4

To find the perimeter of the sector we need to calculate the arc length. To do this we need to know the diameter of the sector.

We can work backwards using the formula for the area of a sector to find the radius to help us find the diameter.

Substituting in what we know,

Now we can calculate the arc length. If the radius is 9cm, the diameter must be 18cm.

For the total perimeter we need to add the two radii to the arc length.

5. What is the sum of the interior angles of a pentagon?

6. A regular polygon has an interior angle of 165^{\circ}. How many sides does it have?

The interior and exterior angle of a polygon sum to 180^{\circ}. We can find the exterior angle using this fact.

To find out the number of sides we then do,

2D shapes GCSE questions

1. The hexagon ABCDEF has one line of symmetry.

2D shapes gcse question 1

Angle FAB = angle ABC = 110^{\circ}.

Angle AFE = angle BCD .

Angle FED = angle CDE .

Angle CDE : angle BCD = 3 : 2.

Find the size of angle AFE .

Indicating sum of angles is 720^{\circ} or 540^{\circ} if line of symmetry used to form a pentagon.

Finding the sum of AFE and FED is 250^{\circ}.

Use of ratio 3:2 or sight of 3x and 2x.

Finding x=50.

Angle AFE = 100^{\circ}.

2. The perimeter of the rectangle is twice the perimeter of the isosceles triangle.

2D shapes gcse question 2

Find the area of the rectangle.

Correct expression for perimeter of rectangle or triangle,

Forming an equation linking the perimeters.

For example, 6x+2=2(2x+5) or equivalent.

Solving equation to get x=4.

Correctly substituted into length and width of rectangle.

Area given as 42cm^{2}.

3. The sector has a perimeter 25cm and radius 6cm.

2D shapes gcse question 3

Find the size of angle x. Give your answer to 3 significant figures.

Sight of arc length given as 13cm.

Process to use formula \frac{x}{360} \times 2 \times \pi \times 6=13

Learning checklist

You have now learned how to:

  • Identify lines of symmetry and order of rotational symmetry in 2D shapes
  • How to work out the perimeter
  • Work out the area of triangles, quadrilaterals and circles
  • Work out the area of compound shapes
  • Identify and apply circle definitions and properties
  • Calculate the circumference of a circle
  • Calculate the area and arc length of a sector 
  • Distinguish between regular and irregular polygon

The next lessons are

  • Pythagoras theorem

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Teaching in the Heart of Florida

Classifying 2D Shapes with Error Analysis Activities

Geometry is one of my favorite standards to teach, and classifying 2D shapes with these fun error analysis activities makes it even better! I think 3rd graders love it, too – because they’ve been playing with shapes their entire life!

problem solving 2d shape

Common Core Standards – 3rd Grade

The Common Core standard for this skill is:

3.GA.1: Understand that shapes in different categories (e.g. rhombuses, rectangles, and others) may share attributes (e.g. having four sides) and that the shared attributes can define a large category (e.g. quadrilaterals). Recognize that rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

What 3rd Graders Know and Need to Know

Coming into 3rd grade, most students know these geometric shapes:

Now, they need to go a step further and learn about how to classify these shapes into categories such as quadrilaterals and equilaterals . Most importantly, they will learn that polygons are plane figures with angles and at least 3 straight sides and that these shapes can be put into different categories.

2D Shapes Reference Chart

One of the tools that I think really helps students learn the attributes of these shapes and categories is to create an anchor chart with them. But I also like to give each student a Plane Shapes Reference Chart for their math notebook. With these in hand, they pretty quickly learn all the names of the plane shapes along with their attributes.

problem solving 2d shape

Hands-On 2D Shapes: Sorting and Classifying

Hands-on math activities are a great way to engage students and reinforce their understanding of key math concepts. When it comes to teaching geometry, 2D shapes are a fundamental concept that can be reinforced through hands-on activities. Sorting and classifying 2D shapes is a great way to help students identify their attributes and understand their characteristics.

Using hands-on activities, such as pattern block manipulatives or cut-out shapes, students can sort and classify the shapes based on their attributes, such as the number of sides, angles, and symmetry.

By allowing students to manipulate physical objects, they can better visualize and understand the attributes and characteristics of 2D shapes.

Problem Solving Activities

Once students have learned attributes for the 2D shapes and have had time to sort and classify them by the number of sides, the number of angles, and whether they have sets of parallel lines, they are ready to take it up a notch.

One of the activities that I love to use for that added rigor is error analysis. I LOVE error analysis! Error analysis math activities are more engaging for students because they challenge them to think critically and identify errors in problem-solving. This type of activity also provides an opportunity for students to work collaboratively and communicate their reasoning, which leads to deeper learning and retention of mathematical concepts.

BUT – the best part of this – KIDS love to find errors!

Classifying 2D Shapes Error Analysis Activity

This set of 36 error analysis task cards is formatted to give your students multiple ways to classify 2D shapes. Using their reference chart, your students will determine if the attributes listed on the task card are true or false.

problem solving 2d shape

You can use these task cards in several ways:

2D Shapes True or False Sorting Activity

problem solving 2d shape

2D Shapes Error Analysis – Why is it true or false?

The way they will work this out is on the worksheet pictured below. They will complete these steps:

  • Draw and label the shape(s).
  • List their attributes.
  • Determine if the statement was true or false.
  • Write to explain and defend their decision using geometry vocabulary.

problem solving 2d shape

You are going to LOVE seeing how they learn to write about their math thinking AND how this activity encourages them to use math vocabulary!

The task cards have several different options for how they compare and classify plane shapes and include triangles which are not part of the standard – but help them differentiate (and classify) the number of sides and angles versus quadrilaterals.

This classifying 2D shapes error analysis resource will add another level of rigor to your math activities. When introducing error analysis – start at the whole group level by modeling your thinking. Then give students support as they work on this activity. Finally – put it in your math centers. Students can practice this activity multiple times to get the most benefit from it.

If you would like to use an activity with a high level of rigor that includes writing in math – click here.

problem solving 2d shape

After your students have mastered the skill of classifying and sorting 2D shapes and you want to review with them – this fun 2D Shapes Jeopardy game is the perfect whole-group activity! Kids love to play Jeopardy games , and this one gives them the fun and the important review all in one!

problem solving 2d shape

Thanks for reading!

The most valuable resource that all teachers have is each other. Without collaboration our growth is limited to our own perspectives. Robert John Meehan

problem solving 2d shape

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problem solving 2d shape

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Area of 2D Shapes – Definition, Formulas & Examples

What is the area of 2d shapes, area of 2d shapes using formula, area of 2d figures by counting squares, solved examples on area of 2d shapes, practice problems on area of 2d shapes, frequently asked questions on area of 2d shapes.

Area of a 2D shape is the quantity that expresses the region enclosed within the boundary of a two-dimensional shape. 

2D stands for two-dimensional. 2D shapes are shapes with two dimensions, such as width and height. These shapes do not have thickness or height. 

Examples of 2D shapes are square, rectangle, triangle, circle, etc.

2D shapes

How to find the area of 2D shapes? Let’s understand. 

Related Games

Add to Find the Area Game

We can also find the area of 2D shapes using formulas. Different shapes have different formulas for calculating the area. Let’s understand how to find the area of a 2D shape using formula. In this section, you can explore the formulas for the area of 2D shapes.

Area of a Square

A square is a 2D shape with four equal sides and all four angles equal to $90^{\circ}$. 

The area of a square is the product of its two adjacent sides. 

Since all sides of the square are equal.

Area of 2D Shapes – Definition, Formulas & Examples

Area of Square $= \text{Side} \times \text{Side}$

Area of Square $= (\text{Side})^{2}$

Area of a Square $ = \text{s}^{2}$

We can see that while measuring the area of a square, we consider only the length of its side. 

Let’s take an example of the given square and try to find its area. 

Area of a square

Side of the Square $= 4\; \text{cm}$

Area of Square $= (4)^{2} = 16\; \text{cm}^{2}$

Area of a Rectangle

Rectangle is a 2D shape with four sides. Opposite sides of a rectangle are equal and all four angles are equal to $90^{\circ}$. 

The area of a rectangle is the product of its two adjacent sides. 

Rectangle

Area of Rectangle $=$ Length $\times$ Width

Area of Rectangle $= \text{l} \times \text{w}$

We can see that while measuring the area of a rectangle, we consider both the length and width of the rectangle.

For example, we have a rectangle here of length 8 cm and width 3 cm. Let’s try to find its area. 

Rectangle of sides 8 cm and 3 cm

Length of the rectangle, $\text{l} = 8\; \text{cm}$

Width of the rectangle, $\text{w} = 3\; \text{cm}$

Area of the rectangle $= \text{l} \times \text{w}$

Area of the rectangle $= 8 \times 3 = 24\; \text{cm}^{2}$

Area of a Triangle

A triangle is a 2D shape with three sides (edges) and three vertices. A triangle with vertices A, B, and C is denoted as $\Delta$  ABC.

Triangle

For a given triangle, where the height of the triangle is h and the base is b, the area of the triangle can be calculated by the formula:

Area of triangle $= \frac{1}{2} \times$ base $\times$ height

Area of triangle $= \frac{1}{2} \times \text{b} \times \text{h}$

Note that the base and height of the triangle are perpendicular to each other.

There are different types of triangles, like the equilateral triangle, isosceles triangle, and right-angled triangle, but the formula for the area of all kinds of triangles is the same. 

The following image shows base and height for an equilateral triangle, scalene triangle, and right-angled isosceles triangle. Note that the base equals height in a right angled  isosceles triangle.

Types of triangles

Let’s take an example of the given triangle ABC. 

Area of triangle

In the triangle ABC, the base measures 6 units and the height measures 4 units.

Area of triangle ABC $=  \frac{1}{2} \times \text{b} \times \text{h}$

                                  $= \frac{1}{2}  \times 6 \times 4$

                                  $= 12$ sq. units

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Add and Color Shapes (Within 10)

Look at the shapes given below. We won’t be able to use basic formulas to find out the area of such irregular 2D shapes. In order to calculate the area of two dimensional shapes where we cannot apply any formula, we have another method, which is by counting squares on the grid. 

Area of irregular 2D shapes

Now, we know that area is the region inside the boundary of the 2D shape, we can express the area in terms of unit squares . A square whose side is of length 1 unit has an area of 1 square unit. 

1 square unit

To find the area of 2D figures using this method, we count the number of squares that cover the surface of the figure.

While counting the squares, we follow these rules :

  • If the figure is covered by less than half a square, count it as zero.
  • If the figure is covered by more than half a square, count it as 1 unit.
  • If the figure is covered by exactly half a square, count it as $\frac{1}{2}$ a unit.
  • If the figure is covered by a full square, count it as 1 unit.

Let us find the area of the given pentagon.

Pentagon area

Area of the pentagon is the total area of all the squares covered $= 6 + 0 + 0 + 6 = 12$ square units

Area of irregular figures can be easily found using this method.

  • Among all the shapes with the same perimeter, a circle has the largest area.
  • A rectangle with all sides equal is called a square.
  • All squares are rectangles but all rectangles are not squares.
  • Note that the term surface area is used to represent the total area of all the outer faces of a 3D solid figure. Area is the region bounded within the boundaries of a 2D shape. Thus, the surface area of 2D shapes is nothing but the area of a 2D shape.

The next time you want to roll out a grass lawn to cover your front yard, you can find the area of the yard to figure out the size of roll-out lawn needed to make your front yard beautiful.

  • Find the area of the given shape.

Irregular shape

Solution: Let’s count the number of unit squares (completely filled, half-filled, more than half-filled, less than half-filled). Completely filled unit squares are marked in the image below for reference.

Area of irregular shape

Area of the irregular 2D shape is the total area of all the squares covered $= 4 + 0 + 0 + 6 = 10\; \text{m}^{2}$

2. Find the length of the rectangle whose area is $35\; \text{m}^{2}$ and width is 5 m.

Area $= 35\; \text{m}^{2}$

Width $= 5\; \text{m}$

$35 = \text{l} \times 5$

$355 = \text{l}$

$\text{l} = 7\; \text{m}$

Length of the rectangle is 7 m.

3. The floor of a rectangular hall is to be covered with a carpet 200 cm wide. If the length and width of the hall are 20 m and 18 m respectively, find the cost of the carpet at the rate of $2 per meter.

Area of the hall $= 20 \times 18 = 360\; \text{m}^{2}$

Width of the carpet $= 200\; \text{cm} = 200 \div 100 = 2\; \text{m}$

Area of carpet $=$ Area of hall

Therefore, length of the carpet $= \frac{Area of the hall}{Width of the carpet} = \frac{360}{2} = 180\; \text{m}$

Rate of the carpet $= \$2$ per meter

Therefore, cost of the carpet $= \$ (180 \times 2) = \$ 360$

4. Find the area of the given figure.

Area of 2D shape

The given figure can be divided into a square and triangles as shown.

Area of 2D figure

Area of the figure $=$ Area of triangle $1 +$ Area of triangle $2 +$ Area of the square

Area of the triangle $1 =$ Area of the triangle $2  = \frac{1}{2} \times$ base $\times$ height

$= \frac{1}{2} \times 5 \times 6$

$= 15\; \text{m}^{2}$

$= 5^{2} = 25\; \text{m}^{2}$

Area of the figure $= 15 + 15 + 25 = 55\; \text{m}^{2}$

Area of 2D Shapes – Definition, Formulas & Examples

Attend this quiz & Test your knowledge.

Find the area of the hexagon.

Area of 2D Shapes &#8211; Definition, Formulas &amp; Examples

Find the area of a square whose side is 7 cm.

A marble tile measures 30 cm by 20 cm. how many tiles will be required to cover a wall of size 6 m by 2 m, find the area of the given figure..

Area of 2D Shapes &#8211; Definition, Formulas &amp; Examples

What are polygons?

2D shapes that are made up of straight lines and form a simple closed figure are called polygons.

For example, square, rectangle, and triangle are examples of polygons.

Polygons: Square, Rectangle, Triangle

What are regular and irregular polygons?

Regular polygons are polygons with equal sides and angles. Example: equilateral triangle, square, regular pentagon, etc. Irregular polygons are polygons with irregular shapes. Their sides and angles are not equal.

Regular Polygons and Irregular Polygons

Give a real-life application of the area.

Covering a table with a sheet is a real-life application of area of 2D shapes. The whole surface of the table is to be covered with a sheet, so by finding the area of the surface of the table, we can find out the size of the sheet required to cover the surface of the table.

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Properties of 2D shapes including problem solving

Properties of 2D shapes including problem solving

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

salma99

Last updated

6 October 2018

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Draw 2D Shapes Lesson

This Year 2 Draw 2D Shapes lesson covers the prior learning of counting sides and vertices on 2D shapes, before moving onto the main skill of drawing 2D shapes.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

National Curriculum Objective Mathematics Year 2: (2G2a)   Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line

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Lesson Slides

Lesson Slides

These lesson slides guides pupils through the prior learning of counting sides and vertices on 2D shapes, before moving onto the main skill of draw 2D shapes. There are a number of questions to check pupils' understanding throughout.

Modelling PowerPoint

Modelling PowerPoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

Lesson Slides

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

1 Prior Learning

Worksheet

2 Practical Activities

Supporting Activity

Supporting Activity

This Draw 2D Shapes supporting activities sheet contains suggestions for additional tasks you might wish to use to support pupils' understanding of the concepts taught in the lesson.

2 Varied Fluency

Worksheet

This differentiated worksheet includes varied fluency questions for pupils to practise the main skill of this lesson.

Interactive Activity

Interactive Activity

This Year 2 Draw 2D Shapes Game checks pupils' understanding of drawing and creating 2D shapes.

2 Reasoning & Problem Solving

Mixed Practice

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of draw 2D shapes.

Extension

This draw 2D shapes extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the draw 2D shapes lesson.

Worksheet

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

Discussion Problem

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

Interactive Challenge Activity

Interactive Challenge Activity

This Year 2 Draw 2D Shapes Maths Challenge is designed to check pupils' understanding of drawing shapes within a problem solving context.

Worksheet

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Consolidation Pack

Consolidation Pack

These Properties of Shape worksheets are fantastic at helping your pupils practice their reasoning and problem solving skills. This pack contains two different question types for Year 2 Spring Block 3.

Home Learning Pack

Home Learning Pack

This Spring week 8 Maths pack contains varied fluency, reasoning and problem solving worksheets

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problem solving 2d shape

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IMAGES

  1. Problem Solving and Sorting 2-D Shapes in Year 2

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  2. 2d shape problem solving activity

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  3. KS2 Problem Solving Involving 2D Shape

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  5. 2D Shapes Problem Solving Activities by Hanging Around in Primary

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COMMENTS

  1. 2d Shapes Worksheets

    1st Grade Section sorting 2d and 3d shapes identify different types of 2d shapes. drawing shapes using positional language - inside, above, below,... 2nd Grade Section identify and name members of the triangle family, e.g. equilateral triangles. identifying and sorting other 2d shapes

  2. 2D Shapes Practice Questions

    2D Shapes Practice Questions Click here for Questions . Click here for Answers . Practice Questions The Corbettmaths Practice Questions and Answers on 2D Shapes

  3. Playing with 2D Shape

    Giving children chance to 'play around' with two-dimensional shapes gives them the freedom to explore spatial properties for themselves, thereby developing their understanding in a meaningful way. These activities offer contexts in which children can engage in this 'play'. Matching Triangles Age 5 to 7 Challenge Level

  4. Grade 4 Math: Exploring 2D Shapes with Printable Worksheets

    These printable worksheets are designed to reinforce Grade 4 math skills and introduce students to the world of 2D shapes. By exploring 2D Shapes with printable worksheets, your 4 th graders will become more active in recognizing and drawing shapes with their specified attributes like number of sides, angles, etc.

  5. Free printable 3rd Grade 2D shapes worksheets for math practice

    Learning about 2D shapes helps 3rd graders develop spatial awareness, geometry, measurement, and problem-solving skills. It also prepares them for more advanced math topics in the future, such as area, perimeter, fractions, and algebra. ... A 2D shape is flat with only two dimensions: length and width. It does not have any thickness or depth ...

  6. Problem Solving with 2D Shapes mini lesson

    0:00 / 14:58 Introduction Problem Solving with 2D Shapes mini lesson UTES Education 49 subscribers Subscribe 4 91 views 2 years ago 4th Grade Math Review and define 2D shapes, then apply that...

  7. Properties of Shapes KS2

    Age 5 to 11 Challenge Level Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together? Sorting Logic Blocks Age 5 to 11 Challenge Level This activity focuses on similarities and differences between shapes. Seeing Squares Age 5 to 11 Challenge Level

  8. 2D Shapes

    We can solve problems involving 2D shapes using a variety of methods. What are 2D shapes? Polygons Polygons are 2D shapes made from straight lines. You will deal with two different types of polygons. Regular polygons Regular polygons have specific properties. They have all sides of equal length and all interior angles are equal.

  9. Multiplication with 2D Shapes Problem Solving Worksheets

    Use these differentiated problem-solving worksheets to consolidate learning about 2D shapes and related vocabulary. The activities include use of multiplication tables facts up to the ten times table. Why not support pupils who are less confident about properties of 2D shapes by using these 2D Shape Posters display posters on your working wall.

  10. 2D Shapes Challenge Cards (teacher made)

    These multiple-choice task cards engage students in questions about shapes and attributes of shapes. Modeled after testing questions, this resource is perfect for preparing students for test-prep or as a cumulative review. Students will answer questions about triangles, quadrilaterals, pentagons, hexagons, and octagons. Show more Related Searches

  11. 2d shape problem solving activity

    2d shape problem solving activity Subject: Mathematics Age range: 7-11 Resource type: Worksheet/Activity File previews docx, 59.19 KB My Year 5 children were so into this activity they wanted to work through their playtime.

  12. Classifying 2D Shapes with Error Analysis Activities

    Problem Solving Activities Once students have learned attributes for the 2D shapes and have had time to sort and classify them by the number of sides, the number of angles, and whether they have sets of parallel lines, they are ready to take it up a notch. One of the activities that I love to use for that added rigor is error analysis.

  13. Problem Solving 2d Shapes

    Results for ‛Problem Solving 2d Shapes' 476 teaching resources Problem Solving 2d Shapes Sort: Relevance . Grades Grade 1 165. Grade 2 186. Grade 3 207. Grade 4 166. Grade 5 141. Grade 6 104. Grade 7 18. Kindergarten 104. Pre-Kindergarten 38. Resource Types Worksheet 257. Game 78.

  14. Area of 2D Shapes

    Practice Problems on Area of 2D Shapes Frequently Asked Questions on Area of 2D Shapes What Is the Area of 2D Shapes? Area of a 2D shape is the quantity that expresses the region enclosed within the boundary of a two-dimensional shape. 2D stands for two-dimensional. 2D shapes are shapes with two dimensions, such as width and height.

  15. Coordinate Problems With 2D Shapes

    Edexcel Foundation. PPT. PDF. PDF. PPT. PDF. PDF. Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes.

  16. 2d Geometry Problem Solving Teaching Resources

    Hanging Around in Primary. Provide practice during your 2D Shapes Geometry unit with these centers to identify, describe, and manipulate 2D Shapes. These hands-on geometry centers include building 2D shapes, sorting 2D shapes, and problem - solving with 2D shapes. There are 12 Math Centers and 18 worksheets for additional practice.

  17. Multiplication with 2D Shapes Problem Solving Worksheets

    Use these differentiated problem-solving worksheets to consolidate learning about 2D shapes and related vocabulary. The activities include use of multiplication tables facts up to the ten times table. Why not support pupils who are less confident about properties of 2D shapes by using these 2D Shape Posters display posters on your working wall.

  18. Properties of 2D shapes including problem solving

    Properties of 2D shapes including problem solving | Teaching Resources Properties of 2D shapes including problem solving Subject: Mathematics Age range: 7-11 Resource type: Worksheet/Activity File previews docx, 1.11 MB notebook, 389.43 KB smartboard and worksheets on properties of 2d shapes. Creative Commons "Sharealike"

  19. PDF Year 2 Make Patterns with 2D Shapes Reasoning and Problem Solving

    Reasoning and Problem Solving Make Patterns with 2D Shapes Developing 1a. Dan is correct. Various possible answers, for example: All the odd numbered positions in the pattern are triangles and all the even numbered positions are squares. 2a. The pattern drawn should be red triangle, blue circle, red triangle, blue circle repeating. 3a.

  20. 2D Shape Reasoning Challenges (teacher made)

    These 2D Shape Reasoning Challenges are the perfect activity for children to complete in order to challenge their understanding of 2D shapes and support making comparisons! An activity that further develops children's basic understanding of the properties of 2D shapes and supports them in recording full reasoning answers of comparison.

  21. Geometry Word Problems Challenge Cards for revision

    This set of geometry word problems is presented on a set of challenge cards. Download with one easy click, and then print and cut out the cards to begin using them as a challenging work activity. The 7 cards include space for working out and can be kept after use as a revision resource or refresher activity. There is a handy answer sheet in the ...

  22. Problem solving using 2-D representations of 3-D shapes

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  23. Year 2 Draw 2D Shapes Lesson

    This Year 2 Draw 2D Shapes lesson covers the prior learning of counting sides and vertices on 2D shapes, before moving onto the main skill of drawing 2D shapes. ... This Year 2 Draw 2D Shapes Maths Challenge is designed to check pupils' understanding of drawing shapes within a problem solving context. Complete Activity on CS Kids. 2 Homework ...