Perimeter of a Square – Definition – Examples – Formula

What is perimeter?

Perimeter comes from the Greek words ‘Peri’ meaning surrounding or inclosing of a surface and ‘Meter’ meaning distance. So perimeter means total measurement of boundaries of a surface.

Definition:

The Perimeter of a square is the distance (total of length) covered by its boundaries.

The perimeter of a two-dimensional (closed geometrical shape) is calculated by adding its all the sides together.

A square is a closed polygon with four equal sides. Therefore, if we multiply 4 with any of the sides, it will give us perimeter of the square.

It is measure in units, such as m, cm, in, ft, etc.

The perimeter of a square is total length of boundary of a square. So, to calculate the perimeter of a square, we will find the sum of all its sides. All sides of a square are equal.

A square has four sides and they all are equal in length.

A square has four sides and they all are equal in length.

The formula of perimeter of a square = 4 x Side

Derivation of Perimeter of a square formula

In above figure, ABCD is a Square,

Four sides of square are AB, AC, CD and BD, and they are all equal in length.

               Thus,   AB = AC = CD = BD.

Perimeter of a square = sum of the length of its sides.

sum of the length of its sides are AB + AC + CD + BD

If L is the length of a side of square then

Perimeter of a square = L + L + L + L

= 4L

= 4 times the length of a side of a square

= 4 x L 

Solved Examples

Example 1: Find the perimeter of a square whose side is 3 cm.

Solution:

Given: Side L = 3 cm

Perimeter of a square formula = 4L

Substitute the value of L in the formula,

P = 4L

= 4 x 3

= 12 cm

Therefore, the perimeter of the square = 12 cm.

Example 2: Find the perimeter of a square whose side is 9 cm.

Solution:

Given: Side L = 9 cm

Perimeter of a square formula = 4L

Substitute the value of L in the formula,

P = 4L

= 4 x 9

= 36 cm

Therefore, the perimeter of the square = 36 cm.

Example 3: Find the perimeter of a square whose side is 15 cm.

Solution:

Given: Side L = 15 cm

Perimeter of a square formula = 4L

Substitute the value of L in the formula,

P = 4L

= 4 x 15

= 60 cm

Therefore, the perimeter of the square = 60 cm.

Example 4: Find the perimeter of a square whose side is 12 cm.

Solution:

Given: Side L = 12 cm

Perimeter of a square formula = 4L

Substitute the value of L in the formula,

P = 4L

= 4 x 12

= 48 cm

Therefore, the perimeter of the square = 48 cm.

Example 5: If the perimeter of a square is 96 cm, find its side.

Solution:

Perimeter = 4 x side or

Side of a square = 1/4 x perimeter

side of square = 1/4 x 96

= 96/4

= 24 cm

Example 6: If the perimeter of a square is 88 cm, find its side.

Solution: Perimeter = 4 x side or

Side of a square = 1/4 x perimeter

so, side of square = 1/4 x 88

= 88/4

= 22 cm

Example 7: If the perimeter of a square is 120 cm, find its side.

Solution: Perimeter = 4 x side or

Side of a square = 1/4 x perimeter

so, side of square = 1/4 x 120

= 120/4

= 30 cm