Perimeter of Square | Formula, Derivation, Examples

Square is a closed regular polygon where all sides are equal, and all angles are 90° each. Perimeter of a square is defined as the total length of the boundary of that square. 

Let’s learn how to use the formula for the Perimeter of Square with the help of solved examples.

What is Perimeter of Square?

The perimeter of square is the total length of the boundary of its shape.

A square, known for its equal sides and right angles, has a simple formula for calculating its perimeter. The perimeter is calculated by adding the lengths of all four sides.

Since each side of a square is of equal length, the perimeter can be easily calculated by multiplying the length of one side by four.

Perimeter of Square

Perimeter of Square Formula

The perimeter of the Square can be calculated using the following formula,

Perimeter of square = 4 × side

The unit for the perimeter of a square is the unit used for length. It is measured in meters (m), centimeters (cm), inches (in), etc.

Derivation of Perimeter of Square

To derive the perimeter of the square, we are required to add all the sides of the square.

Let us assume the length of the sides is denoted as “a”,

Perimeter = a + a + a + a

⇒ Perimeter of square = 4a

Where a is the side of the square.

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• Perimeter of Square

How to Find the Perimeter of Square?

Perimeter of square can be calculated using these three methods

• Using side length
• Using diagonal
• Using area

Perimeter of Square using Side Length

The below-given steps can be used to find the perimeter of square using side length,

Step 1 : Measure the side of the square.

Step 2 : Multiply the side length by 4.

Step 3 : Express the perimeter obtained in the respective unit.

Perimeter of Square using Diagonal

If the side of the square is not given, but the diagonal is given, then we make use of a different formula.

Diagonal of a square is given by the following formula :

Diagonal of Square

The formula for the Perimeter of square using the diagonal is given below.

Steps to find the area of the perimeter of the square using diagonals :

1. Measure the diagonal of the square.
2. Calculate the perimeter of the square using the formula, P = 4 × (Diagonal/√2).

Perimeter of Square using Area

When the area of square is given, let us assume the area of square is a.

As we all know, Area, a = (side)²

Therefore, the perimeter of the square is,

Steps to find the area of the perimeter of square using area :

1. Measure the area of the square.
2. Calculate the area of the square using the formula, Perimeter = 4 × √Area.

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• Area of square

Perimeter of Square and Rectangle

Square is a special case of rectangles. Perimeter of Rectangle is calculated using the following formula

P= 2× (length+breadth)

where, are the length and breadth are the rectangle’s two distinct sides.

Since the length and breadth are equal in the case of squares,

Perimeter of Square = 2× (length+ length) = 2× ( 2× side) = 4 × side

Related :

• Perimeter of Rectangle
• Perimeter of Geometrical Shapes
• Quadrilateral
• Perimeter of Triangle
• Circumference of a Circle

Perimeter of Square Examples

Let’s solve some example problems on the Perimeter of Square.

Example 1: Find the perimeter of the square if the side given is 4 units. 

Solution:

The Perimeter of square is,

P = 4 × side 

⇒ P = 4 × 4 

⇒ P = 16 units

Example 2: Find the side and perimeter of the square if the diagonal given is 2√2 cm.

Solution:

Side = Diagonal/√2 

⇒ Side = 2√2/√2 

⇒ Side = 2 cm

Perimeter of square = 4×side 

⇒ Perimeter = 8 cm

Example 3: Find the diagonal if the perimeter of the square is 3√2 cm.

Solution:

Perimeter = 4 × (diagonal/√2) 

⇒ (3√2 × √2 ) /4 = diagonal

⇒ Diagonal = 1.5 cm

Example 4: Find the perimeter if the area given is 25 sq units.

Solution:

Perimeter = 4√Area 

⇒ Perimeter = 4√25 

⇒ Perimeter = 20 units

Perimeter of Square Worksheet

Here are a few practice questions on the Perimeter of Square for you to solve.

1. Find the perimeter of a square with a side length of 5 cm.
2. If a square park has a perimeter of 200 meters, what is the length of each side?
3. The perimeter of a square is equal to the perimeter of a rectangle with a length of 15 cm and a width of 10 cm. Find the side length of the square.
4. A square playground has an area of 81 square meters. Calculate the perimeter of the playground.

Perimeter of Square- FAQs

1. What is Perimeter of Square Formula?

The formula for perimeter of square is, P = 4 × Side

2. What is Unit of Perimeter of Square?

The units used for perimeter of square are the units used for length. The units used are meter (m), centimeter (cm), inches (in), etc.

3. What is Area of Square?

Formula used for area of square is, A = Side².

4. How to Find the Side Length of Square When Perimeter is Given?

To find the side length of a square when perimeter is given, we divide the perimeter by 4. This is because all four sides of a square are of equal length, and the perimeter is the sum of all four sides.

5. How to Find Perimeter of Square When Area is Given?

To find the perimeter of a square when the area is given, we first calculate the side length by taking the square root of the area, and then multiply the side length by 4.

Formula: Perimeter = 4 × √Area.