Question

What is the area of a square inscribed in a circle of diameter p cm ?

Answer 1

The diameter of the circle = Diagonal of the square = p
We know that diagonal of a square = $\sqrt{2}a$
$$\begin{gathered} \Rightarrow \sqrt{2}a=p \\ \Rightarrow a=\frac{p}{\sqrt{2}} \end{gathered}$$
Thus, the area of the square = $a^2={\left(\frac{p}{\sqrt{2}}\right)}^2=\frac{p^2}{2}{\mathrm{cm}}^2$