Perimeter of a square is the total length around the edge of the square. We can find the perimeter of a square by adding all its four sides. It is measured in units such as m, cm, in, and ft.

Formulas

Using Side Length

The basic formula to calculate the perimeter of a square is given below:

Derivation

As we know, perimeter of a square is the total length around the boundary of a square. Thus, we need to add all its four sides to find the perimeter.

Mathematically,

Perimeter (P) = sum of all sides

= side + side + side + side

= 4 × side

= 4a, where a = side length

Let us solve some examples to understand the concept better.

Find the perimeter of a square with a side length of9 m

Solution:

As we know, Perimeter (P) = 4a, here a = 9 m = (4 × 9) m = 36 m

If the perimeter of a square is 92 units, find its side

Solution:

As we know, Perimeter (P) = 4a, here P = 92 units => 92 = 4a => a = 92/4 => a = 23 units

Using Diagonal

The formula to calculate the perimeter of a square when only diagonal is known is given below:

Derivation

In square ABCD,

Applying Pythagoras theorem, we get

d^{2} = a^{2} + a^{2}

=> d^{2} = 2a^{2}

=> d = a × √2

=> a = d/√2

Since, Perimeter (P) = 4 × side = 4a

= 4 × d/√2

= 4 × √2d ×/2

= 2√2 × d

Hence,

Perimeter (P) = 2√2 × d

Let us solve an example to understand the concept better.

Find the perimeter of a square with a diagonal of11 cm

Solution:

As we know, Perimeter (P) = 2√2 × d, here d = 11 cm = (2√2 × 11) cm = 22√2 cm

Using Area

The formula to calculate the perimeter of a square when only the area is known is given below:

Derivation

As we know,

Area (A) = (side)^{2 }= a^{2}

=> a = √A

Again, as we know

Perimeter (P) = 4a, here a = side

Perimeter (P) = 4 × √A

Let us solve an example to understand the concept better.

Calculate the perimeter of a square park with an area of 20 cm^{2}.

Solution:

As we know, Perimeter (P) = 4 × √A, here A = 20 cm^{2} = (4 × √20) cm = 4√20 cm Alternative Method As we know, Area (A) = a^{2}, here A = 20 cm^{2} => 20 = a^{2} => a^{2} = 20 => a = √20 cm Now, as we know Perimeter (P) = 4a, here a = √20 cm => (4 × √20) cm => 4√20 cm