# Class 5 Perimeter

## Perimeter

Perimeter is the sum of the lengths of the sides of any figure. Let’s find out perimeter of triangle, rectangle, square and quadrilateral.

## Perimeter of a Triangle

Perimeter of a triangle can be find out by adding the length of it’s three sides. Let’s see some examples.

**Example 1.** Find out the perimeter of the below given triangle.

**Solution.**Length of side AB = 5 cm

Length of side BC = 7 cm

Length of side AC = 5 cm

Perimeter of the triangle = Length of AB + Length of BC + Length of AC

= 5 cm + 7 cm + 5 cm

= 17 cm

So, the perimeter of the triangle is 17 cm.

**Example 2.** Find out the perimeter of the below given triangle.

**Solution.**Length of side AB = 3 cm

Length of side BC = 4 cm

Length of side AC = 5 cm

Perimeter of the above triangle = Length of AB + Length of BC + Length of AC

= 3 cm + 4 cm + 5 cm

= 12 cm

So, the perimeter of the triangle is 12 cm.

## Perimeter of a Rectangle

Perimeter of a rectangle is sum of all four sides. We know that opposite sides of a rectangle are equal.

Perimeter of a rectangle = 2 x (Length + Breadth)

**Example 1.** Find out the perimeter of a rectangle whose length is equal to 5 cm and breadth is equal to 3 cm.

**Solution.**

Perimeter of the rectangle = 2 x (Length + Breadth)

= 2 x (5 cm + 3 cm)

= 2 x 8 cm

= 16 cm

So, the perimeter of the rectangle is equal to 16 cm.

## Perimeter of a Square

Perimeter of a square is sum of all four sides. We know all the sides of a square are equal.

Perimeter of a square = 4 x Side length

**Example 1.** The side of a square is 5 cm. Find the perimeter.

**Solution.**Perimeter of the square = 4 x Side length = 4 x 5 cm = 20 cm.

So, the perimeter of the square is equal to 20 cm.

## Perimeter of a Quadrilateral

Perimeter of a quadrilateral is the sum of the length of all four sides.

Perimeter of the quadrilateral = Length of AB + Length of BC + Length of CD + Length of AD

**Example 1.** Find the perimeter of below given quadrilateral.

**Solution.**Perimeter of the quadrilateral ABCD = 2 cm + 6 cm + 3 cm + 4 cm

= 15 cm

So, the perimeter of the quadrilateral ABCD is equal to 15 cm.

**Example 2.** Find the perimeter of below given figure.

**Solution.** Perimeter of the polygon = AB + BC + CD + DE + EA

= 22 cm + 9 cm + 6 cm + 25 cm + 6 cm

= 68 cm

So, the perimeter of the polygon is 68 cm.

**Example 3.** Find the perimeter of the below given figure.

**Solution.** In the above figure, AF = BE

=> AF = BC + DE

=> 6 cm = BC + 3 cm

=> BC = 3 cm

EF = AB + CD

=> 25 cm = 20 cm + CD

=> CD = 25 cm – 20 cm

=> CD = 5 cm

Perimeter of the above figure = AB + BC + CD + DE + EF + AF

= 20 cm + 3 cm + 5 cm + 3 cm + 25 cm + 6 cm

= 62 cm

**Example 4.** Perimeter of a rectangular field is 528 m. If length of the field is double the length of it’s breadth then find out the length and breadth of the filed.

**Solution.** Perimeter of rectangle = 2 x ( Length + Breadth ) Length = A & Breadth = B

= 2 x (A + B)

Length of the rectangle is double the length of breadth.

A = 2B

=> 2 x (A + B) = Perimeter of rectangle

=> 2 x (2B + B) = 528 cm

=> 2 x (3B) = 528 cm

=> 6B = 528 cm

=> B = 528 ÷ 6

=> B = 88 cm

A = 2B

A = 2 x 88 cm = 176 cm

So, the length of the rectangle is 176 cm and breadth is 88 cm.

**Example 5.** Perimeter of a square field is 556 cm. What is the length of it’s one side?

**Solution.** Perimeter of a square = 4 x A (A = Length of each side)

4 x A = 556 cm

A = 556 ÷ 4 = 139 cm

So, length of each side of the square is 139 cm.

**Example 6.** Perimeter of a triangular field is 145 m. Length of two sides are 35 m and 45 m. What is the length of it’s third side?

**Solution.** Perimeter of a triangle = Total length of all the three sides

= A + B + C

35 m + 45 m + C = 145 m

=> C = 145 – (35 + 45)

=> C = 65 m

So, the length of the third side is 65 m.

**Example 7.** Find the cost of fencing a rectangular field of 70 m length and 50m width at the rate of Rs. 200 per meter.

**Solution.** Perimeter of the rectangular field = 2 x ( Length of the field + Breadth of the field)

= 2 x (70 + 50) = 2 x 120 = 240 m

Fence to be erected on 240 m at a rate of 200 per meter.

Cost of fencing = 240 m x Rs. 200 = Rs. 48000

So, cost of fencing is Rs. 48000

## Perimeter Test

## Class-5 Perimeter Worksheet

## Answer Sheet

**Perimeter-Answer**Download the pdf

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