Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 21, 2023

Area of Square -To calculate the area of a square, multiply the base by itself, which can be expressed as side × side.

Enter the side

### The formula for Area of a Square

The universal formula to calculate the area of a square is-

a²= a*a, where a is equal to the side of the square.

To measure the area of a square, we need to know the length of its sides. All four sides have equal lengths. They are designated by the unit’s measure or centimeter.

### Calculating the Area of a square

The steps required to calculate the area are-

Step 1- Note down the length of sides given in the question

Step 2- Designate the length as ‘a’

Step 3- Write the formula- a²= a*a

Step 4- insert the values given in the question in the way as written in the formula.

Step 5- multiply the given sides.

Step 6- The required results are obtained as a²

### Examples of Finding the Area of a Square

Example 1- Find the area of a square whose side is 85 cm²

Solution-

Step 1- the given side as ‘a’ is 85 cm.

Step 2- a²=a*a

Step 3- 85*85= 7225

Step 4- The area of the square is 7225 cm²

Example 2- We may be asked to find the side of the square. For Example, Find the side of a square whose area is 625 m².

Solution-

Step 1- area= 625 m²

Step 2- a²= √a*a

Step 3- 625= √25

Step 4- the side of the square is 25

Example 3- The percentage of change in the measure of an area can be asked. For example, If each side of a square is increased by 25%, find the percentage change in the area.

Solution-

Let the side of the square be ‘a’. Then, area= a²

New side= 125a/100= 5a/4.

New area= 25a²/16

Increase in the area= (25a²/16 - a²) = 9a²/16

Increase % = 9a²/16 * 1/a² * 100) % =56.25%

Q. What is the requirement to know the area of a square?

A. If the shape of a room is in a square shape, it is necessary to know the area for estimating the total cost of that room.

Q.Is square a polygon?

A. A square is a regular polygon of four sides

Q. Can the area of the diagonal of a square be calculated?

A. The diagonal of the square can be calculated. Its formula is a²= ½(diagonal) ².

Q. If the length of any one side of the square is changed, will the shape remain unchanged?

A. No, the shape of the square will change. It can then be formed into a rectangle.