Perimeter of a Square: Easy Formula, Definitions, and Practical Examples

Perimeter of Square

Perimeter of a Square: In geometry, the perimeter represents the total distance around the outside of a shape. Understanding this fundamental concept is crucial for building a strong foundation in mathematics. Think about real-world scenarios, such as walking around the edge of a square park; to find the distance you traveled, you would need to calculate the sum of all four sides of that park.

What is the Perimeter of a Square?

The perimeter of a square is defined as the total length of its boundary. Because a square is a regular polygon with four equal sides, calculating the distance around it simply requires multiplying the length of one side by four. 

Perimeter of Square Formula

Mathematically, the formula for calculating the perimeter of a square is expressed as follows:

Since all four sides of a square are equal in length,

Then, the Perimeter of the square = 4 × Side

Derivation of Perimeter of Square 

Because a square maintains equal sides, the perimeter is consistently four times the length of a single side.

Perimeter (P) = Sum of the lengths of all sides of a closed figure

Perimeter of Square = Side + Side + Side + Side

Perimeter of Square = 4(S)

In this formula, “S” represents the length of one side of the square.

Calculation of Perimeter of Square

The perimeter of a square can be determined using different properties depending on the information provided. The table below outlines the various methods for calculating this value. 

Calculation of Perimeter of Square
Parameters	Formula
Using Side Length	Perimeter = 4 × Side
Using Diagonal	Perimeter = (√2 × diagonal/2) × 4 = (2√2 × diagonal) units.
Using Area of Square	Perimeter = (√area) × 4 = 4√area units.

 Examples of Perimeter of Square 

Q1. If the perimeter of a square is 72 units, what is the length of its side?

Solution: Given, perimeter of the square = 72 units.

Using the formula: Perimeter = 4 × Side

72 = 4 × Side

Side = 72 / 4

Side = 18 units

Q2. If the side of a square is increased by 8 meters, its area increases by 120 sq. meters. Find the original side length and the perimeter.

Solution: Let the length of each side of the square be ‘x’ meters.

We know the area of a square is defined as (Side × Side).

According to the problem, the new side = (x + 8).

The new area is expressed as: Area = x² + 120.

Therefore, the equation is: Area = (Side)² 

x² + 120 = (x + 8)² 

x² + 120 = x² + 16x + 64

120 = 16x + 64

120 - 64 = 16x

 56 = 16x

x = 56 / 16

x = 3.5

So, the side of the original square is 3.5 meters.

Calculating the perimeter: Perimeter = 4 × Side

Perimeter = 4 × 3.5

Perimeter = 14 Units 

Q3. Given the area of a square is 289 square units, calculate its perimeter using the standard formula.

Solution: Area of square = 289 square units.

Formula: Area = (side)²

289 = (side)²

Side = √289

Side = 17 Units

The side of the square is 17 units. 

Perimeter = 4 × Side

Perimeter = 4 × 17

Perimeter = 68 Units