## Square Definition, Properties, Area, and Perimeter.

## Definition of Square

A square is a two-dimensional shape with four equal sides and four right angles (90 degrees each). It is a regular quadrilateral, which means that all four sides are of equal length and all four angles are of equal measure.

## The properties of a square

- All four sides are of equal length.
- All four angles are equal and right angles (90 degrees).
- It has four corners.
- The sum of all interior angles is 360°.
- The diagonals are of equal length and bisect each other at right angles.
- The length of the diagonals in a square is greater than its sides.
- The perimeter of a square is equal to 4 times the length of one of its sides.
- The area of a square is equal to the length of one of its sides squared.

## Area

The area of a square is calculated by multiplying the length of one side by itself.

Area of square(A) = side length(S) x side length(S)

Or

Area of square = (side length)

^{2}

Let’s understand by an example

**Q 1. A square has a side length of 5 meters. Then find the area of a square.**

Area of square = side length x side length

Area of square = 10 x 10

Area of square = 100 square meters.

Or

Area of square = (side length)^{2}

Area of square = (10)^{2}

Area of square = 100 square meters.

## Perimeter

The perimeter of the square is calculated by four times of side.

Perimeter of square = 4 x side length

let’s understand by an example

**Q 1. A square has a side length of 5 meters. Now, find its perimeter.**

Perimeter of square = 4 x side length

Perimeter of square = 4 x 5

Perimeter of square = 20 meters.

## Diagonals of square

The diagonal of a square is a line that connects two opposite corners of the square. It is the longest line in the square. The diagonals of a square are equal in length and bisect each other at a right angle.

Diagonal of square = side length x √2

**[ root 2 value = 1.414]**

Let’s understand by an example

**Q 1. A square has a side length of 5 meters. Find the length of the diagonal.**

Diagonal of square = side of length x √2

Diagonal of square = 5 x √2

Diagonal of square = 5 x 1.414 = 7.07m

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