Geometry Math Problems - Perimeters

In these lessons, we will learn to solve geometry math problems that involve perimeter.

Related Pages Geometry math problems involving area Area Formula Geometry math problems involving angles More Algebra Word Problems

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Geometry Word Problems Involving Perimeter

Example: A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Solution: Step 1: Assign variables:

Let x = length of the equal sides Sketch the figure

Step 2: Write out the formula for perimeter of triangle .

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

50 = x + x + x+ 5

Combine like terms 50 = 3x + 5

Isolate variable x 3x = 50 – 5 3x = 45 x = 15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 = 20

Answer: The length of third side is 20.

Geometry Math Problem involving the perimeter of a rectangle

The following two videos give the perimeter of a rectangle, a relationship between the length and width of the rectangle, and use that information to find the exact value of the length and width.

Example: A rectangular garden is 2.5 times as long as it is wide. It has a perimeter of 168 ft. How long and wide is the garden?

Example: A rectangular landing strip for an airplane has perimeter 8000 ft. If the length is 10 ft longer than 35 times the width, what is the length and width?

Examples of perimeter geometry word problems This video shows how to write an equation and find the dimensions of a rectangle knowing the perimeter and some information about the about the length and width.

Example: The width of a rectangle is 3 ft less than its length. The perimeter of the rectangle is 110 ft. Find the dimensions.

Perimeter Word Problems

Example: The length of a rectangle is 7 cm more than 4 times its width. Its perimeter is 124 cm. Find its dimensions.

Geometry Math Problem involving the perimeter of a triangle

The following two videos give the perimeter of a triangle, a relationship between the sides of the triangle, and use that information to find the exact value or values of the required side or sides.

Example: Patrick’s bike ride follows a triangular path; two legs are equal, the third is 8 miles longer than the other legs. If Patrick rides 30 miles total, what is the length of the longest leg?

Example: The perimeter of a triangle is 56 cm. The first side is 6 cm shorter than the second side. The third side is 2 cm shorter than twice the length of the first side. What is the length of each side?

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Positional Words

Identify Objects Above and Below Game

Identify Objects Above and Below Game

Learn to solve problems by identifying objects 'above' and 'below'.

Counting Objects Above and Below Game

Counting Objects Above and Below Game

Begin the exciting journey of becoming a math wizard by counting objects 'above' and 'below'.

Front and Behind Worksheet

Front and Behind Worksheet

Practice 'Front' and 'Behind' by printing this playful worksheet.

Above and Below Worksheet

Above and Below Worksheet

Practice 'Above' and 'Below' by printing this playful worksheet.

Find Right Angles Game

Find Right Angles Game

Take the first step towards building your math castle by practicing how to find right angles.

Identify Right Angles Game

Identify Right Angles Game

Enjoy the marvel of mathematics by identifying right angles.

Identify Trapezoids Worksheet

Identify Trapezoids Worksheet

Make math practice a joyride by identifying trapezoids.

Separate Out the Trapezoids Worksheet

Separate Out the Trapezoids Worksheet

Put your skills to the test by practicing to separate out the trapezoids.

Coordinate Planes

Identify the Missing Coordinate Game

Identify the Missing Coordinate Game

Add more arrows to your child’s math quiver by identifying the missing coordinate.

Identify the Coordinates of the Point Game

Identify the Coordinates of the Point Game

Kids must identify the coordinates of the point to practice geometry.

Spot the Decimals on a Number Line Worksheet

Spot the Decimals on a Number Line Worksheet

Reveal the secrets of math wizardry by practicing to spot the decimals on a number line.

Identify Ordered Pairs On Coordinate Grid Worksheet

Identify Ordered Pairs On Coordinate Grid Worksheet

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Geometry Proofs List

Table of contents.

29 October 2020                

Read time: 7 minutes

Introduction

Geometry is the study of visualizations. Perceiving what objects/ images mean/ signify is a major part of the work in this area of study.

Children often struggle with geometry since it is a jump from the basic concepts of algebra into something more abstract and unique. And because it is so different from what children have learned before, the art of teaching it should vary too.

Unfortunately, the school curriculum does not account for that and goes on teaching in the same format. The small inconvenience of not being able to understand a concept stems from something stronger and severe as children grow - the fear of geometry & math.

If your child struggles with geometry , it could be for the following reasons:

  • Unable to understand & apply the vocabulary to decode the problem.
  • Can’t see or imagine all of the pieces that go into making up the Geometry problem.
  • Struggle with the Algebra skills involved in doing Geometry

But even if learning geometry comes easy to them, one thing that the whiz kids find tough is with proofs!

And what better way to help sort these proofs out than a geometry proofs list compiling the list of geometry proofs and references to geometry proofs.

Children's doing Geometry math's

Geometry proofs are what math actually is. To put it simply- they're the explanation , and everything else follows from them. This means they're the most important part of the whole field by a very large measure, but they're generally going to be more difficult than anything else.

We are going to share an important geometry proofs list, that your children should be familiar with. And also explain how to solve geometry proofs.

Worry not, Cuemath has a way around that to ensure every child not only learns proofs and applies them, but also loves the process of learning them.

We have attached corresponding topic links in the geometry proofs list and statements mentioned for a deeper understanding of each.

If your children have been learning geometry, they would be familiar with the basic proofs like the definition of an isosceles triangle, Isosceles Triangle Theorem, Perpendicular, acute & obtuse triangles, Right angles, ASA, SAS, AAS & SSS triangles.

, ASA, SAS, AAS & SSS triangles

All of these proofs, like anything else, require a lot of practice . They're inherently different from solving problems because you already know the result and are solving for it. All kids need to do is manipulate the logic and structures after understanding how to solve these geometry proofs.

Here are some geometric proofs they will learn over the course of their studies:

Parallel Lines

If any two lines in the same plane do not intersect, then the lines are said to be parallel.

Certain angles like vertically opposite angles and alternate angles are equal while others are supplementing to each other.

Parallel Lines

Corresponding Angles

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Vertical Angles

States, “If two non-adjacent angles are created by intersecting lines, then those angles are known as vertical angles.”

The Definition of Isosceles Triangle

Says that “If a triangle is isosceles then TWO or more sides are congruent.”

Isosceles Triangle Theorem

Says that “If a triangle is isosceles, then its BASE ANGLES are congruent.” This applies to the above point that you have already learned.

BASE ANGLES are congruent

Acute Triangle/ Obtuse Triangle

Says that “If a triangle is an acute triangle, then all of its angles are less than 90 degrees.”

And, “If a triangle is an obtuse triangle, then one of its angles is greater than 180 degrees.”

Perpendicular

States “If two lines, rays, segments or planes are perpendicular, then they form right angles (as many as four of them).”

Right Angle/ Acute Angle/ Obtuse Angle

States, “If an angle is a right angle, then the angle must EQUAL 90 degrees.”

“If an angle is an acute angle, then the angle must be less than 90 degrees.”

“If an angle is an obtuse angle, then the angle must be greater than 90 degrees.”

Congruency of Triangles: ASA, SSS, SAS, AAS

States, if the two angles and the side included between them of one triangle are equal to the two corresponding angles and the side included between them of another triangle, the two triangles are congruent.

ASA Triangle

states, if the three sides of one triangle are equal to the three corresponding sides of another triangle, the two triangles are congruent.

SSS Triangles

says that “If two sides and an included angle of one triangle are congruent to two corresponding sides and an included angle of another triangle, then the triangles are congruent.”

States, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent.

says that “If two angles and non-included sides of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.”

AAS Triangle

Angle-Angle (AA) Similarity

If the three angles of one triangle are respectively equal to the three angles of the other, then the two triangles will be similar

SSS for Similarity

if the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.

SAS for Similarity

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar

States that “If you use ASA, SSS, SAS, or AAS to prove that two triangles are congruent, then all other corresponding parts (sides & angles) of the congruent triangles are going to be congruent.”

Reflexive Property

States, “something is congruent to itself.”

Segment Addition Postulate/ Angle Addition Postulate

used when we do part + part = whole (for either sides or angles).

Interior angles of Triangle

Adding up all the interior angles of a triangle gives 180º

Interior angles of Triangle

Segment Bisector

States “If a segment, ray, line or plane is a segment bisector, then it divides a segment into TWO equal parts.”

Definition of Altitude

States, “If a segment is an altitude, then it is a segment originating from one of the vertices of a triangle and its perpendicular to an opposite side.”

Altitude

Exterior Angle

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles and the value is greater than either non-adjacent interior angle.

Exterior Angle

Circle Proofs used

The radius of a circle is always perpendicular to a chord, bisects the chord and the arc.

A tangent dropped to a circle, is perpendicular to the radius made at the point of tangency.

tangent dropped to a circle

Tangent segments from a single point to a circle at different points are equal.

An angle inscribed in a semi-circle or half-circle is a right angle.

This was the important geometry proofs list.

This list of geometry proofs form the base to other proofs and theorems that your child will learn. It is essential for children to learn & pay attention to the general styles of proofs so that they would be able to apply it to other problems.

Once they get thorough with the geometry proofs list, they would get an intuition for how different structures act and interact and what strategies might be best to apply..this way they won't even find geometry hard, and will be able to solve the complete list of geometry proofs.

How to solve geometry proofs?

Now that we know the importance of being thorough with the geometry proofs list, here is how you can get your children to tackle the list of geometry poofs.

1. Plan it out

Einstein once said that if he had 60 min to solve a problem, he would spend 58 minutes defining the problem statement. Defining the problem statement helps with planning , and as experts say, planning is the first step to tackling a problem.

tackling a problem

Familiarize your children with the importance of planning right. Teach them to start by writing out the problem in plain English, with no mathematical jargon. Solving Geometry proofs just got a lot simpler.

2. Look for lengths, angles, and keep CPCTC in mind

All the geometry concepts your child has learned would come to life here. They could start by allocating lengths for segments or measures for angles & look for congruent triangles.

3. Parallel Lines can be a lifesaver

This is an old trick that you would be familiar with as well. Any parallel lines in the proof’s diagram mean that you would use one of the parallel-line theorems.

Pass on this wisdom to help your children solve geometry proofs given in the geometry proofs list.

Parallel Lines

4. If-then logic is always gold

Another one from the bag of tricks, ‘all the ideas in the if clause appears in the statement column somewhere above the line you‘re checking’.

This theory also helps to figure out what reason to use in the first place. This can work on any one of the theorems in the geometry proofs list!

5. If you get stuck, work backward

Jump to the end of the proof and start making guesses about the reasons for that conclusion. You can almost always figure out the way by using the if-then logic to reach the previous statement (and so on).

work backward

Geometry proofs don't have to be hard for the kids, but we hope that with the right guidance, they will be familiar with how to solve geometry proofs. The geometry proofs list, along with tips on how to solve geometry proofs can be a good start to train your child and get them to love geometry.

Written by Sonia Motwani

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Math competition no problem for mms students, team headed for state mathcounts meet in march.

learn geometry solve problems

Photo by Deb Gau Members of the Marshall Middle School math team, including Nathan Larsen, Lauren Paulson, Katelyn Moberg and Clara Purrington, and coach Tara Ryks spoke about their activity at the Marshall School Board meeting on Tuesday.

MARSHALL — They get up early in the morning and solve math problems for fun. And the efforts of students on the Marshall Middle School math team have paid off — a group of team members are headed for the state MathCounts competition in the Twin Cities in March.

Learning new math skills and ways to solve problems was one of the fun things about being part of the team, students said.

“For me, it’s the satisfaction of seeing how things come together,” said MMS student Nathan Larsen. The team is always learning about something new, he said.

“I also love learning new things,” said Clara Purrington. She remembered feeling excited learning new math strategies when she started competing with the team in sixth grade. “I thought, ‘I need to keep going with this,.”

A group of math team members, along with coach Tara Ryks, talked about their season with the Marshall School Board this week, as well as with the Independent.

The MMS math team includes students in grades 6-8, Ryks said.

“For me and some of the other people on the team, I think we always had an interest in math,” said student Lauren Paulson. She and some of her teammates have been competing together since they were in sixth grade.

This year, about 24 students were on the math team, Ryks said.

“We usually start up at the end of October and run through early February,” she said.

Students meet once a week at 7:15 a.m. — or even earlier — to learn new math strategies and solve problems together, Paulson said.

“Each week, two students take turns bringing doughnuts to provide for the math team,” she said.

Katelyn Moberg said the team competes in five virtual meets through the Minnesota Junior High Math League, and then they have an in-school competition to help determine which 15 students will go to the Southwest Chapter MathCounts Competition.

The regional MathCounts competition was held earlier this month. The MMS team placed first overall, and a total of eight students were recognized for top individual honors. Five students advanced to the state competition: Larsen, Moberg, Paulson, Purrington, and Emily Rosenboom.

Larsen and teammate Moberg both competed at the state MathCounts tournament last year, as well.

“It was amazing,” Moberg said. Besides the math competition, students also enjoyed a supper with a pasta bar, and did some fun group contests focused on engineering. Moberg said last year, students teamed up with kids from other schools to build catapults.

The state competition will include two individual rounds of math problems, one team round, and a timed “countdown round,” Ryks said.

Competing in the countdown round could be stressful, students said.

“You’re trying to figure out how to do a problem in like, 10 seconds,” Larsen said.

Moberg said it would probably be less stressful this year, now that she had been to state before.

Ryks said it’s been fun to work with the math team and co-coach Samantha Tauer.

“It’s a total blast,” she said. The students are some of the hardest-working kids at MMS, she said.

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How do you solve a problem like a gopher? Fountain Valley is learning through experience

A Jan. 9 photo taken near Fountain Valley's Westmont Park shows evidence of burrowing gophers, a problem in some city parks.

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How do you solve a problem like a gopher? In the city of Fountain Valley, rodents digging networks of subterranean tunnels that compromise the soil integrity of local parklands have been an ongoing challenge for public works employees.

“They burrow all day long, so there are shallow tunnels that can create risks if they do cave in,” said Mark Sprague, a field services manager for the city. “They mostly feed on the roots of plants. They also chew irrigation lines. It’s caused a lot of problems both privately and publicly.”

Visitors to Los Alamos Park, Harper Park and the city’s Sports Park near Mile Square Regional Park — identified by city staff as gopher “hot spots” — may have seen signs of the rodent’s presence in the area, including cones and markers placed near tunnels.

A photo taken by Fountain Valley's Public Works Department shows cones placed near gopher tunnels at Los Alamos Park.

Officials have for years contracted with an area landscaping company to trap and remove the critters. But recently, an observed increase in gopher activity is popping up in residential neighborhoods.

Fountain Valley City Councilman Jim Cunneen said it’s common for residents to air gopher grievances at City Hall, sometimes speaking in public comments at council meetings, or to bring up the subject at local functions.

“It’s not unique to our city, but something has triggered a rise in the population of gophers in our parks,” he said Friday. “A lot of people in our neighborhood are dealing with gophers. You can see it in some of the front lawns of our neighbors.”

Cunneen has lived for the past three decades near the city’s Los Alamos Park on a street named La Marmota Avenue, the Spanish word for groundhog. Although he recalled having issues with the animals in the ’90s, his backyard was pretty calm until the recent population explosion.

“We have at least 30 holes gophers have chewed,” he said. “They take out a 3- to 4-inch diameter patch, and they’re also burrowing so the surface becomes uneven — it’s horrible.”

Gopher Mitigation Update https://t.co/zG5HUgmcwh pic.twitter.com/Njt8PAPLOr — City of Fountain Valley (@fv_cityhall) February 7, 2024

City officials reported last week on social media gopher mitigation efforts are in full swing at local parks. Where a typical month may bring in 15 to 20 animals, last month more than 40 trappings were logged, according to Sprague.

Cunneen said extermination companies tend not to deal with gophers, requiring residents to seek out services that offer to remove the animals by trapping them. It’s unclear, however, what happens once an animal is captured.

Representatives of Merchants Landscape Services, which handles landscaping for Fountain Valley and its more than 150 acres of park space under an $873,000 annual contract, did not immediately respond to a request for that information. But one local wildlife expert offered some advice.

Debbie McGuire, executive director of the nonprofit Wetlands & Wildlife Care Center in Huntington Beach, maintains state laws prohibit the relocation of many small animals and rodent species into different habitats. She said many removal companies end up humanely euthanizing the animals they trap.

One explanation for the rising gopher population may be a decline in the presence of predators who feed on them, such as bobcats and coyotes or birds of prey like barn owls.

A photo taken in Fountain Valley's Courreges Park in November shows a gopher popping up from an underground tunnel.

“Gophers are really important for the ecosystem. They move the soil around and keep roots aerated so plants stay healthy,” McGuire said Friday. “But there are times when there are no predators to keep their population down, and they’ll get out of control.”

She suggested city employees or residents in Fountain Valley might look into installing nesting boxes in public parks and residential neighborhoods to attract animals like the barn owl, which prey on gophers but leave larger animals, like cats and dogs, undisturbed.

A number of organizations and resources can be found online, including the Barn Owl Box Co. , which sells nesting boxes and instructs people how to build their own.

“The best thing is to leave nature alone and let the circle of life take care of things,” McGuire advised.

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Sara Cardine covers the city of Costa Mesa for the Daily Pilot. She comes from the La Cañada Valley Sun, where she spent six years as the news reporter covering La Cañada Flintridge and recently received a first-place Public Service Journalism award from the California News Publishers Assn. She’s also worked at the Pasadena Weekly, Stockton Record and Lodi-News Sentinel, which instilled in her a love for community news. (714) 966-4627

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