Question

A square whose diagonal is $10cm$ long has an area equal to

Answer 1

Let the side of the square is $a$

The diagonal of the square $=10cm$

$$\begin{gathered} \sqrt{2}a=10 \\ a=\frac{10}{\sqrt{2}} \end{gathered}$$

The side of the square $=\frac{10}{\sqrt{2}}$

Area of square $=side\times side$

$$\begin{gathered} =\frac{10}{\sqrt{2}}\times \frac{10}{\sqrt{2}} \\ =\frac{100}{2} \\ =50 \end{gathered}$$

Hence, the area of square is $50c{m}^2$.