Question

Find the area of a square whose diagonal is $5\sqrt{2}$ cm.

Answer 1

Area of the square =$\left\{\frac{1}{2}\times (D\mathrm{iagonal}{)}^2\right\}\mathrm{sq}\mathrm{units}$
$$\begin{gathered} =\left\{\frac{1}{2}\times (5\sqrt{2}{)}^2\right\}{\mathrm{cm}}^2 \\ =\left\{\frac{1}{2}\times (5{)}^2\times (\sqrt{2}{)}^2\right\}{\mathrm{cm}}^2 \\ =\left\{\frac{1}{2}\times 25\times 2\right\}{\mathrm{cm}}^2 \\ =(\frac{1}{2}\times 50){\mathrm{cm}}^2=25{\mathrm{cm}}^2 \end{gathered}$$