Question

The length of the diagonal of a square is d. the area of the square is

(a) d² (b) $\frac{\text{1}}{\text{2}}{\mathit{\text{d}}}^{\text{2}}$ (c) $\frac{\text{1}}{4}{\mathit{\text{d}}}^{\text{2}}$ (d) 2d²

Answer 1

Let a be the side of the square. Then
Diagonal of the square = $\mathit{\text{a}}\sqrt{2}$
Therefore
$$\begin{gathered} a\sqrt{\mathit{2}}=d\Rightarrow a=\frac{d}{\sqrt{2}} \\ \therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{square}={\left(\frac{d}{\sqrt{2}}\right)}^2=\frac{d^2}{2} \end{gathered}$$
Hence, the correct option is (b).