# Perimeter of Square

## Trigonometry # Perimeter of Square

The perimeter of a square is the total length covered by its boundary, in a plane. Perimeter is the path that encompasses a shape. The perimeter of a closed geometrical shape (two-dimensional) is calculated by adding all the sides together. A square is a four-sided polygon, thus its perimeter of the square will be equal to the sum of all its four equal sides. Here, we have given a detailed explanation of the perimeter of the square, formula and derivation along with solved examples.

## What is Perimeter of a Square?

The perimeter of any closed geometrical object is defined as the distance around that object. The perimeter of a square is the distance covered by its four sides.  Perimeter surrounds or outlines the shape in a two-dimensional plane.

Since all the sides of a square are equal, therefore, the perimeter of square will be 4 times its side, i.e. 4 × Side. It is measured in units, such as m, cm, in, ft, etc.

## Perimeter of Square Formula

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

 Perimeter of Square (P) = 4 × Side

### Example: If length of side of square is 3cm, then find its perimeter.

Perimeter of square = 4 x side = 4 x 3 = 12 cm.

## Derivation of Perimeter of Square Formula

The perimeter of the square is defined as the total length of the boundary of a square. We need to add all the sides of square to find its perimeter. By the formula of perimeter of polygon, we know;

Perimeter = sum of all sides

Perimeter of square = Sum of the lengths of 4 sides

= side + side + side + side

= 4 × side

Therefore, the perimeter of Square = 4s units

Where, s = Length of a side of the square

## How to Find Perimeter of Square?

We have already learned to calculate the perimeter of the square using the formula,

Perimeter = 4 × side

But if the length of the side of square is not given, then we can calculate the perimeter of square, if two we are given with either of two details:

1. Length of diagonal of square
2. Area of square

Let us figure out, how we can find the perimeter using diagonal and using area.

### Perimeter of Square Using Diagonal

As we know, a square is regular polygon that has all sides equal. Also, all the four angles of square are 90 degrees. Thus, we get the length of diagonal of square, using Pythagoras theorem, as:

Diagonal = Side.√2

Thus, the side of square can be written as:

Side = Diagonal/√2

or

Side of square = √2(Diagonal/2)

As we know,

Perimeter of square = 4 x side = 4 x √2(Diagonal/2)

 Perimeter of square = 2√2(Diagonal) units.

Hence, we can find the perimeter using diagonal of square.

 Example: Find the perimeter of square, whose diagonal length is 10 cm. By using the above formula, we have; Perimeter = 2√2(Diagonal) = 2√2(10) = 20√2 cm.

### Perimeter of Square Using Area

The area of a square is defined as the space occupied by the square. The formula for area of square is given by:

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

where “s” is the length of one side.

Now, we can write, side of the square w.r.t. area,

side = √Area

Hence, the perimeter of square will be:

 Perimeter = 4 x side = 4 √Area units.

Thus, we can find the perimeter of a square given its area.

 Example: If area of square is 16 sq.cm. Find its perimeter. Using the above formula, we have; Perimeter = 4 √Area = 4 √16 = 4 x 4 = 16 cm.

## Solved Examples on Perimeter of Square

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

Solution:

Given:

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.

Solution:

Given,
Side of the square = a = 16 cm

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

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

Solution:

Perimeter = 4 × side

Or, Side of Square = ¼ × perimeter

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

## Practice Questions on Perimeter of square

1. What is the perimeter of square, whose side is equal to 11 cm?
2. If length of side of square is 5.5 cm, then find its perimeter.
3. The length of diagonal of a square is equal to 9 cm. Find its perimeter. (Use: √2 = 1.414)
4. If the area of square is 100 sq.in., find its perimeter.

## Frequently Asked Questions

### What is the Perimeter of a Square?

The perimeter of a square is defined as the total distance around the outside of the square. So, it can be said that a square’s perimeter is its total boundary.

### How to Find the Perimeter of a Square?

To calculate the perimeter of a square, add all the sides of it. There are 4 sides of a square which are all equal in length. The sum of the sides will give its perimeter. We can use also find the perimeter of square if the length of diagonal or area of square is given to us.

### What is the Formula for the Perimeter of a Square?

The formula for the perimeter of a square is, P = Side + Side + Side + Side

Or, P = 4 × Side

### What is the unit of perimeter of square?

Perimeter of square is the total distance enclosed by its sides. Perimeter is measures in units such as meters (m), centimeters (cm), inches (in), etc.

### What is area of a square?

The area of a square is the region that the square covers in a two-dimensional space. The area of a square can also be defined as the number of square units it takes to fill the square.