Question

The length of the diagonal of the square is 10 cm. The area of the square is

• A. 20 $c{m}^2$
• B. 100 $c{m}^2$
• C. 50 $c{m}^2$
• D. 70 $c{m}^2$

Answer 1

Answer: (C)

50 $c{m}^2$

Diagonal of square $=10cm$

Also, diagonal of square $=\sqrt{2}\times side$

or, $\sqrt{2}\times side=10\Rightarrow side=\frac{10}{\sqrt{2}}=\frac{10\sqrt{2}}{2}=5\sqrt{2}cm$

$\therefore$ Area of square $={\left(side\right)}^2={\left(5\sqrt{2}\right)}^2=50{cm}^2$