Question

The length of the diagonal of a square is 20 cm. It area is
(a) 400 cm²
(b) 200 cm²
(c) 300 cm²
(d) $100\sqrt{2}$ cm²

Answer 1

(b) 200 cm²
Area of the square = $\left\{\frac{1}{2}\times (\mathrm{Diagonal}{)}^2\right\}\mathrm{sq}\mathrm{u}\mathrm{nits}$
$$\begin{gathered} =\left\{\frac{1}{2}\times (20{)}^2\right\}{\mathrm{cm}}^2 \\ =\left\{\frac{1}{2}\times \left(20\right)\times \left(20\right)\right\}{\mathrm{cm}}^2 \\ =(20\times 10){\mathrm{cm}}^2 \\ =200{\mathrm{cm}}^2 \end{gathered}$$