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 = \[\sqrt{2}a\] 

\[\Rightarrow \sqrt{2}a = p\]
\[ \Rightarrow a = \frac{p}{\sqrt{2}}\]

Thus, the area of the square = \[a^2 = \left( \frac{p}{\sqrt{2}} \right)^2 = \frac{p^2}{2} {cm}^2\]