AREA OF SQUARE FORMULA, DERIVATION – MINDSPARK

Area of Square

A square is a quadrilateral with equal sides. A quadrilateral means a figure having four sides. A square has 4 sides where all the sides and angles are equal. The area of a square means the measure of the surface covered by the square, which is equal to the product of its two sides i.e., a^{2} where a is the side of the square.

First, we take a square of side 5 cm. Now we make vertical and horizontal lines of width 1 cm. After following the above steps, it will form a figure as given below.

The area of each small square will be 1 \times 1=1 \mathrm{~cm}^{2}.

Since there are 25 small squares in the bigger square, the total area will be 25 \mathrm{~cm}^{2}.

Which is also the product of its sides (5 x 5).

After calculating we get the total number of small squares as

25=5 \times 5=a \times a=a^{2}

Therefore, we can say that area of a square =a \times a=a^{2}.

Examples

1. Find area covered by a square whose side is 10 cm.

Solution:

Area of square =a \times a=a^{2}.

Here side of the square is 10 cm.

Therefore, the area of the square =10 \times 10=10^{2}=100 \mathrm{~cm}^{2}

2. If the area of a square is 625 \mathrm{~cm}^{2}then find the side of the square.

Solution:

Area of square =a \times a=a^{2}.

It is given that area of the square is 625 \mathrm{~cm}^{2}.

a^{2}=625

\therefore a=\sqrt{625}=25

We get a = 25 cm.

Hence side of the square is 25 cm.