Perimeter of Square

The perimeter of a square is the length that its boundary covers. The perimeter of a square is obtained by adding all the sides together. Here, the concepts about the perimeter of the square are covered including its formula and derivation along with solved example questions.

What is the Perimeter of a Square?

The perimeter of any closed geometrical object is defined as the distance around that object i.e. the length of its boundary. For a square, the perimeter is calculated by adding its four sides. But, since all the sides of a square are equal, its perimeter will be 4 times its side i.e. 4 × side.

The formula for Perimeter of a Square

Perimeter of Square (P) = 4 × side

Derivation of a Square’s Perimeter

The perimeter of the square is defined as the length of the boundary of a square.

The Perimeter of the square formula is given by,

Perimeter = length of 4 sides

= side+side+side+side

= 4 × side

Therefore, the perimeter of Square = 4s units

Perimeter of Square

Perimeter of Square

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Below is a brief recall about a square and its area.

What is Square?

A square is a quadrilateral in which it has 4 equal sides and all the interior angles of a square are right angles. It is a closed two-dimensional plane figure.

Area of Square

The area of a square is defined as the space occupied by the two-dimensional figure called square and the area of the square formula is given as

Area = width × height

But since the width and height are the same, the formula is usually written as

Area of a Square = Side × side = side² square units

where “s” is the length of one side.

Area Of Square

Does Square have Surface Area?

People sometimes confuse the area of a square with the surface area. The surface area is however for three dimensional figures such as a cube where there is more than one surface are involved and not for the planar shapes such as a square having only a single surface.

Thus, in order to calculate the surface area of the square one must follow the same method as to compute the area of the square.

Solved Problems Using Perimeter of Square Concept

Question 1: Find the perimeter of a square whose side is 5 cm?



Side, s = 5 cm

The formula to find the perimeter of a square is given by

The perimeter of Square = 4s units

Substitute the value of ‘s’ in the perimeter formula,

P= 4 × 5 cm

p = 20 cm

Therefore, the perimeter of square = 20 cm

Question 2: Calculate the perimeter of a square having a side of 16 cm?


Side of the square = a = 7 cm

Perimeter of a Square = 4a
= 4 × 16
= 64 cm

Question 3: If the perimeter of a square is 92 cm, find its sides.


Perimeter = 4 × side

Or, Side of Square = ¼ × perimeter

So, side of the square = 92/4 = 23 cm.

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