# Perimeter of a Square

We will discuss here how to find the perimeter of a square. Perimeter of a square is the total length (distance) of the boundary of a square.

In a square all the sides are of equal lengths.

Hence, perimeter of a square = 4l

We know that all the sides of a square are equal.

Perimeter of the square ABCD

= AB + BC + CD + AD

= 2 cm + 2 cm + 2 cm + 2 cm

= (2 × 4) cm

= 8 cm

Perimeter of a square is 4 times of s side.

Perimeter of a square = 4 × length of a side.

A square is a four sided figure in which

● all the four sides are equal (length = breadth)

● all the angles are equal to 90° (right angle)

1st method:

Perimeter of a square PQRS

= side + side + side + side

= 5 cm + 5 cm + 5 cm + 5 cm

= 20 cm

2nd method:

Perimeter of a square = 4 times side

= 4 × side

= 4 × 5 cm

= 20 cm

Therefore, Perimeter of a square = 4 × length of one side

Word Problems on Perimeter of a Square:

Let us consider some of the examples on perimeter of a square:

1. Each side of a square is 2.5 cm. Find its perimeter.

Solution:

Side = 2.5 cm

Therefore, perimeter of a square = 4 × length of a side

= (4 × 2.5) cm

= 10 cm

2. A rope of length 96 m was used to fence a square garden. What is the length of the side of the garden?

Solution:

Perimeter of the garden = Length of the rope = 96 m

We know that perimeter of a square = 4 × length of a side

So, 4 × length of a side = 96 m

Length of a side = $$\frac{96}{4}$$ m = 24 m

Therefore, length of the one side of the square shape garden is 24 m.

3. Find the perimeter of a square shaped playground whose each side length 12 m.

Solution:

We know a square has four equal sides. So, we can easily calculate the perimeter of a square.

The formula for finding the perimeter of a square is:

P = 4 × length of a side

= 4 × 12 m

= 48 m

4. Each sides of a paper sheet is 14 ft. Find its perimeter.

Solution:

Given: Side length is 14 ft.

Perimeter of a square is = 4 × side

= 4 × 14 ft

= 56 ft

5. Find the perimeter of the square PQRS whose one side is 10.5 m.

Solution:

Side of the square = 10.5 m

Perimeter of the square = 4 × side

= 4 × 10.5

= 42 m

6. Find the perimeter of the square PQRS whose one side is 4 cm.

Solution:

The perimeter of the square

= 4 × side

= 4 × 4 cm

= 16 cm

7. The perimeter of a square is 20 cm. Find the length of each side of the square.

Solution:

Perimeter of the square            =   4 × side of the square

i.e. 4  side of the square           =   20 cm

But we have 4 × 5                   =   20   (Note: 20 × 4 = 5)

Therefore, side of the square    =   5 cm

8. How to find the perimeter of a square?

Find the perimeter of the figure:

Solution:

A square has four sides.

To find the perimeter of a square, we measure all the four sides of the figure and add them together.

In the above given figure, all the sides length = 4 cm

Therefore, perimeter of the square = 4 cm + 4 cm + 4 cm + 4 cm

= 16 cm

Worksheet on Perimeter of a Square:

1. Find the perimeter of squares having sides as follows.

(i) 8 cm

(ii) 6 cm

(iii) 10 cm

(iv) 12 cm

(v) 15 cm

1. (i) 32 cm

(ii) 24 cm

(iii) 40 cm

(iv) 48 cm

(v) 60 cm

2. The perimeter of a square photo frame is 12 cm. What is the length of its side?

2. 3 cm

3. A square has a perimeter of 24 cm. What is the length of each side?

3. 6 cm

4. Find the perimeter of each of the following square using formula:

4. (i) Perimeter of the square 24 cm.

(ii) Perimeter of the square 28 cm.

(iii) Perimeter of the square 24 cm.

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