## Perimeter of Square

**Perimeter of Square: **Perimeter of any geometrical shape is the sum of all the sides. The concept of Perimeter is usually found in lower grades and understanding becomes very important so as to have a good foundation in mathematics. The perimeter has its application in the day-to-day, suppose you went for walk in the park and later you are asked to calculate the perimeter of the park. Now, guess how will you calculate the perimeter of the park. So the shape of the park is square, then the perimeter of the park will be the sum of all sides of the park.

## What is the Perimeter of a Square?

Perimeter of the Square is defined as the sum of all sides of the square. It is calculated by covering the total path of the geometrical shape. As we know square is a four-sided polygon. A square has all four sides equal, so the perimeter is four times the length of each side of a square.

## Perimeter of Square Formula

Mathematically, the formula for the Perimeter of a Square is, it is expressed as-

As we know the sides of the square are equal,

Then, the **Perimeter of the square = 4 × Side**

## Derivation of Perimeter of Square

A square has all four sides equal, so the perimeter is four times the length of each side of a square.

Perimeter (P)= Length of all sides of a closed figure

Perimeter of Square = Side + Side + Side + Side

**Perimeter of Square = 4(S)**

Where “S” means the side of the square.

## Calculation of Perimeter of Square

The Perimeter of the Square is calculated differently based on different parameters. Below is the table which gives you the formula to calculate the perimeter of the square.

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 the square is 72 Units. Then what will be the side of the square?**

**Solution: **Perimeter of the square = 72 Units,

As we know, Perimeter = 4 × Side

72 = 4 × Side

Side = 72/4

**Side = 18 Units**

**Q2. If the side of the square is increased by 8 m, its area increases by 120 sq.m. Find the side of the square and its Perimeter.**

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

As we know the area of the square is = (Side × Side)

According to the question, Side = (x + 8)

and the area is, Area = x² + 120

Therefore, Area = (Side)²

x² + 120 = (x + 8)²

x² + 120 = x² + 16x + 64

120 = x² + 16x + 64 - x²

120 = 16x + 64

16x = 120-64

16x = 56

x= 56/16

x= 4

So the side of the square is 4 meter

Perimeter = 4 x Side

**Perimeter = 16 Units **

**Q3. The area of a square is given as 289 square units. With the help of the perimeter of a square formula, calculate its perimeter.**

**Solution: **Area of square =289 square units.

area of a square = (side)²

289 = (side)²

Side = √289

Side = 17 Units

So the side of the square is 17 Units

Perimeter = 4 x Side

Perimeter = 4 x 17

**Perimeter = 68 Units**