# Perimeter of Square

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 of 9 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

d2 = a2 + a2

=> d2 = 2a2

=> 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 of 11 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 = a2

=> 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 cm2.

Solution:

As we know,
Perimeter (P) = 4 × √A, here A = 20 cm2
= (4 × √20) cm
= 4√20 cm
Alternative Method
As we know,
Area (A) = a2, here A = 20 cm2
=> 20 = a2
=> a2 = 20
=> a = √20 cm
Now, as we know
Perimeter (P) = 4a, here a = √20 cm
=> (4 × √20) cm
=> 4√20 cm