A square’s perimeter is described as the total length of its boundary. The distance around any restricted geometrical shape is used to calculate its perimeter. The perimeter of a square can indeed be calculated by adding all of its sides. It is 4 times the height of every side of the square because all 4 sides of a square are equal. In this article, we will learn about the perimeter of a square in depth.

What is the Perimeter of a Square?

A shape’s perimeter would either be a path that outlines the structure (in 2 dimensions) or rather its length (one-dimensional). A square’s perimeter can be determined by adding the lengths of all its sides.

There are a few properties of a square such as:

  • A square’s angles are always the same as well as equal 90º.
  • A square’s sides are all equal.

Formula

The formula for calculating the perimeter of square is expressed mathematically as:

The perimeter of the square = 4A

A = length of the side

Example 1: What will be the perimeter of a square with a side measuring 5 cm. Using the formula

Solution: A = 5cm

Hence, the perimeter =4A

P=4*5cm

P=20 cm

Therefore, the perimeter of the square with a side of length 5 cm is 20 cm.

Example 2: What will be the side of a square if the perimeter of the square is 40cm.

Solution: If the perimeter of a square is 40 cm

Then, according to the formula 4A = 40cm

A = 10 cm

Hence the length of the side is 10 cm.

Derivation of the formula

The perimeter of a square is described as the sum total length of a square’s boundary. We can find the total of all of the square’s sides to calculate its perimeter. Because all sides of the square are equal, considering the side of the square “a” according to which the perimeter will be given;

Perimeter of the square = A + A + A + A units

Hence the formula of the perimeter of a square can be termed as = 4A

How can we find the perimeter of a Square?

We can find the perimeter of a square under different circumstances using alternative methods which depend upon various factors. Some of the methods of calculating perimeter are using:

  • Using side length.
  • Using area
  • Using Diagonal

Using Side Length

In this case, we usually find the square’s perimeter by multiplying the side length by 4. While finding the perimeter of a square using the side length, we need to follow a few steps that are:

  • Write down the length of the side.
  • Then let’s multiply the side length of the square by 4.
  • The answer obtained is the perimeter of the square and express it with the right unit.

Using Area of a Square

The perimeter of a square can be found by just using the area of that square. While finding out the perimeter using the area of a square, we need to follow these certain steps:

  • Write down the square’s area.
  • Then we continue by finding out the length of the square using the formula = (Area of the square)
  • The value which is derived after using the above formula must be multiplied by 4 in order to find out the value of the perimeter.

Using the diagonal of a Square

The diagonal of a square can also be used to find out the perimeter of a square. While using the diagonal to find out the perimeter of the square we need to follow these steps:

  • Write down the length of the diagonal of the square.
  • Using the length of the diagonal, find out the side of the length of the square. Side = diagonal/√2
  • After obtaining the value of the side, multiply the side by 4 in order to find out the value of the perimeter of the square.

Solved Example

Example 1: What will be the perimeter of a square with a side measuring 8 cm. Using the formula

Solution: A = 8cm

Hence, the perimeter =4A

P=4*8cm

P=32 cm

Therefore, the perimeter of the square with a side of length 8 cm is 32 cm

Example 2: Find out the perimeter of the square using the area = 36 cm2.

Solution: Side = √Area

Side = √36cm

Side = 6 cm

The perimeter of the square = 4*6

The perimeter of the square = 24 cm (Ans)