Area of Square

In this page area of square we are gong to see how to find area of the given square.

Definition of square:

Area enclosed by the 4 equal sides is called the area of the square.

In the following shape ABCD the length of all sides are equal. 


Area of the square = a²

Here a means the length of the side.

Now let us see some example problems to understand this topic.

Example 1:

Find the area of the square having side length 24 cm.


Area of the square = a²

                          = 24² 

                          = 24 x 24

                          = 576 cm²

Example 2:

A square is of area 64 cm². Then its side length.

 Area of the square = 64 cm²

                       a² = 64 cm²

                       a = √64

                         = √8 x 8

                         = 8 cm

Example 3:

The square having side length 25 cm. Find the area of the square in meter.


Area of the square = a²

                          = 25² 

                          = 25 x 25

                          = 625 cm²

               100 cm = 1 m

                          = 625/100

                          = 6.25 m²

Example 4:

Find the area of the square whose diagonal is measuring 4cm.


In the above square we have two right triangles. Triangle ACB and the triangle ADC. In triangle ACB right angled at B. So the side which is opposite to this side is called the hypotenuse side. Since it is square the length of 4 sides will be equal.

By using Pythagorean theorem

AC² = AB² + BC²

4² = x² + x²

16 = 2x²

2x² = 16

x² = 16/2

x² = 8

x = √8

x = √2 x 2 x 2

x = 2√2 cm

Therefore the length of all sides = 2√2 cm

Area of square = a²

                          = (2√2)²

                          = 2²(√2)²

                          = 4 (2)

                          = 8 cm²

Related Topics

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

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Area of Square to Formulas for Shapes