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

## 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

1. All four sides are of equal length.
2. All four angles are equal and right angles (90 degrees).
3. It has four corners.
4. The sum of all interior angles is 360°.
5. The diagonals are of equal length and bisect each other at right angles.
6. The length of the diagonals in a square is greater than its sides.
7. The perimeter of a square is equal to 4 times the length of one of its sides.
8. 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.