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.

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.

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.