Class 5 - Perimeter of a Triangle: Complete Learning Guide

Perimeter of a triangle are important shapes in geometry. In this lesson, Class 5 students will learn the perimeter of a triangle, simple formulas, solved examples, and fun practice worksheets.

Table of Contents

• What is Perimeter of a Triangle?
• Perimeter of Triangle Formula
• Types of Triangles and Their Perimeter
• Solved Examples on Perimeter of a Triangle
• Practice Questions on Perimeter of a Triangle for Class 5
• Perimeter of a Triangle Worksheet for Class 5

What is Perimeter of a Triangle?

The perimeter of a triangle is the total distance around the triangle. It is the sum of the lengths of all three sides of the triangle. When you add the measurements of all the outer edges of a triangle, you get its perimeter.

Perimeter of Triangle Formula

The formula to find the perimeter of a triangle is very simple and easy to remember.

FORMULA:

Perimeter of Triangle = Side 1 + Side 2 + Side 3

In short form:

P = a + b + c

Here:

P stands for perimeter

a, b, and c are the lengths of the three sides of the triangle

How To Find Perimeter

To find the perimeter of a triangle, follow these simple steps:

1. Identify the length of the first side of the triangle

2. Identify the length of the second side of the triangle

3. Identify the length of the third side of the triangle

4. Add all three lengths together

5. Write the answer with the correct unit of measurement

Types of Triangles and Their Perimeter

There are different types of triangles based on their sides and angles. Let us understand each type and how to find their perimeter.

1. EQUILATERAL TRIANGLE

An equilateral triangle is a triangle where all three sides have equal length. All three angles in an equilateral triangle are also equal. Each angle measures sixty degrees.

Formula for Perimeter of Equilateral Triangle:

P = 3a

Here, a is the length of one side. Since all sides are equal, we multiply one side by three.

Example: If one side of an equilateral triangle is 5 centimeters, then the perimeter is 3 × 5 = 15 centimeters.

2. ISOSCELES TRIANGLE

An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called legs, and the third side is called the base. The two angles opposite the equal sides are also equal.

Formula for Perimeter of Isosceles Triangle:

P = 2a + b

Here, a is the length of each equal side, and b is the length of the base.

Example: If the two equal sides of an isosceles triangle are 6 centimeters each and the base is 4 centimeters, then the perimeter is 2 × 6 + 4 = 12 + 4 = 16 centimeters.

3. SCALENE TRIANGLE

A scalene triangle is a triangle where all three sides have different lengths. No two sides of a scalene triangle are equal. All three angles are also different from each other.

Formula for Perimeter of Scalene Triangle:

P = a + b + c

Here, a, b, and c are the lengths of the three different sides.

Example: If the three sides of a scalene triangle are 3 centimeters, 4 centimeters, and 5 centimeters, then the perimeter is 3 + 4 + 5 = 12 centimeters.

4. RIGHT ANGLED TRIANGLE

A right angled triangle is a triangle with one angle of ninety degrees. The side opposite the right angle is called the hypotenuse. This is the longest side in a right angled triangle.

Formula for Perimeter of Right Angled Triangle:

P = a + b + c

Here, a and b are the two perpendicular sides, and c is the hypotenuse.

Example: If the two perpendicular sides of a right angled triangle are 3 centimeters and 4 centimeters, and the hypotenuse is 5 centimeters, then the perimeter is 3 + 4 + 5 = 12 centimeters.

Solved Examples on Perimeter of a Triangle

1: Finding Perimeter of a Scalene Triangle

Problem: A triangle has sides of lengths 7 centimeters, 8 centimeters, and 9 centimeters. Find the perimeter of the triangle.

Solution:

We know that Perimeter = a + b + c

Here, a = 7 cm, b = 8 cm, c = 9 cm

Perimeter = 7 + 8 + 9 = 24 cm

Answer: The perimeter of the triangle is 24 centimeters.

2: Finding Perimeter of an Equilateral Triangle

Problem: An equilateral triangle has each side measuring 6 meters. What is the perimeter of this triangle?

Solution:

We know that Perimeter = 3a (for equilateral triangle)

Here, a = 6 m

Perimeter = 3 × 6 = 18 m

Answer: The perimeter of the equilateral triangle is 18 meters.

3: Finding Perimeter of an Isosceles Triangle

Problem: An isosceles triangle has two equal sides of 10 centimeters each and a base of 6 centimeters. Calculate the perimeter.

Solution:

We know that Perimeter = 2a + b (for isosceles triangle)

Here, a = 10 cm, b = 6 cm

Perimeter = 2 × 10 + 6 = 20 + 6 = 26 cm

Answer: The perimeter of the isosceles triangle is 26 centimeters.

4: Finding Missing Side Using Perimeter

Problem: A triangle has two sides of 5 meters and 7 meters. If the perimeter is 18 meters, find the length of the third side.

Solution:

We know that Perimeter = a + b + c

Here, Perimeter = 18 m, a = 5 m, b = 7 m, c = ?

18 = 5 + 7 + c

18 = 12 + c

c = 18 - 12

c = 6 m

Answer: The third side of the triangle is 6 meters long.

5: Finding Perimeter of a Right Angled Triangle

Problem: A right angled triangle has perpendicular sides of 6 centimeters and 8 centimeters. The hypotenuse is 10 centimeters. What is its perimeter?

Solution:

We know that Perimeter = a + b + c

Here, a = 6 cm, b = 8 cm, c = 10 cm

Perimeter = 6 + 8 + 10 = 24 cm

Answer: The perimeter of the right angled triangle is 24 centimeters.

6: Comparing Perimeters of Different Triangles

Problem: Triangle A has sides 4 cm, 5 cm, and 6 cm. Triangle B is an equilateral triangle with each side 5 cm. Which triangle has a greater perimeter?

Solution:

For Triangle A: Perimeter = 4 + 5 + 6 = 15 cm

For Triangle B: Perimeter = 3 × 5 = 15 cm

Answer: Both triangles have the same perimeter of 15 centimeters.

7: Finding Perimeter with Decimal Measurements

Problem: A triangle has sides measuring 3.5 meters, 4.2 meters, and 5.3 meters. Find the perimeter.

Solution:

We know that Perimeter = a + b + c

Here, a = 3.5 m, b = 4.2 m, c = 5.3 m

Perimeter = 3.5 + 4.2 + 5.3 = 13 m

Answer: The perimeter of the triangle is 13 meters.

8: Word Problem on Triangle Perimeter

Problem: Ravi has a triangular garden with sides of 12 meters, 15 meters, and 18 meters. He wants to build a fence around the entire garden. How much fencing material does he need?

Solution:

To find how much fencing is needed, we need to find the perimeter of the triangular garden.

Perimeter = 12 + 15 + 18 = 45 meters

Answer: Ravi needs 45 meters of fencing material.

9: Finding Perimeter of an Equilateral Triangle with Fractions

Problem: An equilateral triangle has each side measuring 2 and one-half centimeters. What is the perimeter?

Solution:

We know that Perimeter = 3a (for equilateral triangle)

Here, a = 2.5 cm

Perimeter = 3 × 2.5 = 7.5 cm

Answer: The perimeter of the triangle is 7.5 centimeters.

10: Finding Side Length from Perimeter

Problem: An isosceles triangle has a perimeter of 32 centimeters. The base is 8 centimeters. What is the length of each equal side?

Solution:

We know that Perimeter = 2a + b (for isosceles triangle)

Here, Perimeter = 32 cm, b = 8 cm, a = ?

32 = 2a + 8

32 - 8 = 2a

24 = 2a

a = 24 ÷ 2

a = 12 cm

Answer: Each equal side of the isosceles triangle is 12 centimeters long.

Practice Questions on Perimeter of a Triangle for Class 5

1. A triangle has sides of 3 cm, 4 cm, and 5 cm. Find the perimeter.

2. An equilateral triangle has each side measuring 7 cm. What is its perimeter?

3. An isosceles triangle has two equal sides of 9 cm each and a base of 5 cm. Calculate the perimeter.

4. A triangle has sides of 6 meters, 8 meters, and 11 meters. Find the perimeter.

5. A right angled triangle has sides of 5 cm, 12 cm, and 13 cm. What is its perimeter?

6. Priya has a triangular piece of cloth. The sides of the cloth are 10 cm, 12 cm, and 14 cm. What is the perimeter of the cloth?

7. A triangle has sides measuring 4.5 meters, 6.5 meters, and 7 meters. Find the perimeter.

8. Ravi draws a triangle with all three sides equal to 8 inches each. What is the perimeter of his triangle?

9. A triangular park has sides of 15 meters, 20 meters, and 22 meters. If someone jogs around the entire park once, how much distance does he cover?

10. A triangle has sides of 2.5 cm, 3 cm, and 4.5 cm. Find the perimeter.

11. Triangle A has sides 5 cm, 6 cm, and 7 cm. Triangle B is equilateral with each side 6 cm. Which triangle has the greater perimeter?

12. A triangular frame is made with sides of 9 cm, 12 cm, and 15 cm. What is the perimeter of the frame?

13. If a triangle has a perimeter of 24 cm and two sides are 7 cm and 8 cm, what is the third side?

14. A triangle has sides measuring 3.5 cm, 4.5 cm, and 6 cm. Find the perimeter.

15. An equilateral triangle has a perimeter of 18 cm. What is the length of each side?

Perimeter of a Triangle Worksheet for Class 5

Perimeter of a Triangle Worksheets Class 5 Easy

Perimeter of a Triangle Worksheets Class 5 Medium

Perimeter of a Triangle Worksheets Class 5 Hard