3) Which triangle has a perimeter of $ 41 $ units?

Perimeter of a Triangle - Math Steps, Examples & Questions

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Math resources Geometry Perimeter

Perimeter of a triangle

Here you will learn how to find the perimeter of a triangle, including what the perimeter is, how to calculate it and how to solve perimeter word problems.

Students will first learn how to find perimeter as part of measurement and data in 3rd grade.

What is the perimeter of a triangle?

The perimeter of a triangle is the total distance around the outside of the triangle.

For example,

Perimeter is measured in units, like inches.

Measuring the perimeter is like starting at one vertex of a triangle and measuring the total distance around the triangle.

The perimeter can also be calculated by adding the length of each side.

$7 + 7 + 3 = 17,$ so the perimeter is $17$ inches.

What is the perimeter of a triangle?

Common Core State Standards

How does this relate to 3rd grade math?

Grade 3 – Measurement and data (3.MD.D.8)
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

How to find the perimeter of a triangle

In order to calculate the perimeter of a triangle:

Add all the side lengths.
Write the final answer with the correct units.

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How to find perimeter examples

Example 1: perimeter of an isosceles triangle

What is the perimeter of the triangle?

Add all the side lengths.

To find the perimeter (the total distance around the triangle), add all the side lengths:

$9 + 9 + 12 = 30$

2Write the final answer with the correct units.

The side lengths are measured in feet, so the total perimeter is in feet.

The perimeter of the triangle is $30$ feet.

Example 2: perimeter of a right triangle

What is the perimeter of the triangle?

Add all the side lengths.

To find the perimeter (the total distance around the triangle), add all the side lengths:

$12 + 20 + 16 = 48$

Write the final answer with the correct units.

The side lengths are measured in millimeters, so the total perimeter is in millimeters.

The perimeter of the triangle is $48$ millimeters.

Example 3: perimeter of a scalene triangle

What is the perimeter of the triangle?

Add all the side lengths.

To find the perimeter (the total distance around the triangle), add all the side lengths:

$11 + 17 + 8 = 36$

Write the final answer with the correct units.

The side lengths are measured in centimeters, so the total perimeter is in centimeters.

The perimeter of the triangle is $36$ centimeters.

Example 4: perimeter of equilateral triangle

What is the perimeter of the triangle?

Add all the side lengths.

To find the perimeter (the total distance around the triangle), add all the equal side lengths:

$16 + 16 + 16 = 48$

For the perimeter of an equilateral triangle, since the sides of the triangle are the same (congruent), you can also multiply one side length by $3.$

$3 \times 16 = 48$

Write the final answer with the correct units.

The side lengths are measured in meters, so the total perimeter is in meters.

The perimeter of the triangle is $48$ meters.

Example 5: triangle perimeter word problem

A triangular street sign has side lengths of $18$ inches, $18$ inches and $16$ inches. What is the perimeter of the sign?

Add all the side lengths.

To find the perimeter (the total distance around the triangle), add all the side lengths:

$18 + 18 + 16 = 52$

Write the final answer with the correct units.

The side lengths are measured in inches, so the total perimeter is in inches.

The perimeter of the sign is $52$ inches.

Example 6: right scalene triangle

The perimeter of the triangle is $75{~cm}.$ What is the missing side length?

Add all the side lengths.

To find the perimeter (the total distance around the triangle), add all the side lengths:

$\begin{aligned} & 17 \, + \, 31 \, + \,? = 75 \\\\ & 48 \, + \, ? = 75 \end{aligned}$

The two sides together are $48.$ The third side is missing.

To find the missing side, think about what number added to $48$ is $75.$

Since $48 + 27 = 75,$ the missing side length is $27.$

Write the final answer with the correct units.

The side lengths are measured in centimeters and the total perimeter is in centimeters.

The missing side length of the triangle is $27$ centimeters.

Teaching tips for the perimeter of a triangle

Choose worksheets that have a variety of question types – varying the types of triangles – equilateral, isosceles and scalene (therefore varying the lengths of the sides), solving for the perimeter or a missing side length, word problems with or without visuals.

Give students opportunities to measure and solve problems for the perimeter of triangles in the real world.

Easy mistakes to make

Thinking the order of adding the sides matters
It doesn’t matter the order in which the sides of the triangle are added, because of the commutative property of addition. As long as all sides are added only once, they can be added in any order.

Confusing the formulas or solving strategies for perimeter with area
It is easy to confuse these two concepts, especially when first learning them. Remember that perimeter is the measurement of the length around a triangle (one-dimensional), and area is the measurement of the space within a triangle (two-dimensional).

Adding uncommon units
Side lengths need to be the same units before they can be added. If the sides are shown with different units, convert them to a common unit and then add.

Practice perimeter of a triangle questions

36{~ft}

32{~ft}

26{~ft}

54{~ft}

The perimeter (the total distance around the triangle) is the sum of the lengths of the three sides:

$9 + 15 + 12 = 36$

The sides are measured in feet, so the perimeter is also in feet.

The perimeter is $36$ feet.

18{~cm}

84{~cm}

78{~cm}

68{~cm}

The perimeter (the total distance around the triangle) is the sum of the lengths of the three sides:

$18 + 18 + 42 = 78$

The sides are measured in centimeters, so the perimeter is also in centimeters.

The perimeter of triangle $ABC$ is $78{~cm}.$

Perimeter of a Triangle image 10 US

Perimeter of a Triangle image 11 US

Perimeter of a Triangle image 12 US

Perimeter of a Triangle image 13 US

Since the perimeter of the triangle is $41$ units, the length of its sides should add up to $41.$

Perimeter of a Triangle image 14 US

$17 + 17 + 7 = 41$

This triangle has a perimeter of $41$ units.

three sides of $20{~cm}$

12{~cm}, \, 13 {~cm}, \, 14{~cm}

15{~cm}, \, 20{~cm}, \, 15{~cm}

20{~cm}, \, 5{~cm}, \, 20{~cm}, \, 5{~cm}

A triangle has $3$ sides. The perimeter of a triangle is the sum of the $3$ side lengths:

$15 + 20 + 15 = 50$

The sides of a triangle $15{~cm}, 20{~cm},$ and $15{~cm}$ have a perimeter of $50{~cm}.$

$17$ inches

$22$ inches

$15$ inches

$19$ inches

The perimeter (the total distance around the triangle) is the sum of the sides:

$\begin{aligned} & 31 \, + \, 17 \, + \, ? = 67 \\\\ & 48 \, + \, ? = 67 \end{aligned}$

The two sides together are $48.$ The third side is missing.

To find the missing side, think about what number added to $48$ is $67.$

Since $48 + 19 = 67,$ the missing side length is $19$ inches.

$5$ meters

$13$ meters

$41$ meters

$15$ meters

Each side of an equilateral triangle is the same length, so all sides of the large garden are $23$ meters and all sides of the smaller garden are $18$ meters.

Large Garden: Small Garden:

Perimeter of a Triangle image 16 US

Perimeter: Perimeter:

$23+23+23=69$ meters $\hspace{1.1cm} 18+18+18=54$ meters

To find the difference between the perimeter of the large and small garden, subtract:

$69 \, – \, 54 = 15$

The difference in perimeter is $15$ meters.

Perimeter of a triangle FAQs

How do you calculate the perimeter of different types of triangles?

Since all triangles have $3$ sides, just add the length of all three sides to find the perimeter. There are additional ways to solve for different types of triangles, like equilateral and isosceles triangles.

For equilateral triangles, multiply the length of one side by $3.$ For isosceles triangles, multiply one of the equal sides by $2$ and then add the third side.

How do you calculate the area of a triangle?

The area of a triangle can be calculated with the formula: $\cfrac{1}{2} \times b \times h.$

Can the given sides of a triangle be fractions or decimals?

Yes, triangles can have measurements that include fractions or decimals. The perimeter is found the same way – by adding all the sides.

What is the pythagorean theorem?

It is a theorem that relates to right-angled triangles and the relationship between the two sides that form a $90$ -degree angle and the long side, called the hypotenuse. This is a topic covered in middle school.

The next lessons are

Symmetry
Angles in polygons
Congruence and similarity
Prism shape

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