Is the area of the circle inscribed in a square of side $a \, cm$ equal to $\pi a^2 \, cm^2$? Give reasons for your answer.

(N/A) False.
Let $ABCD$ be a square of side $a$.
The circle is inscribed in the square,so its diameter is equal to the side of the square.
$\therefore \text{Diameter of circle} = a \, cm$.
$\therefore \text{Radius of circle} (r) = \frac{a}{2} \, cm$.
Now,the area of the circle is given by the formula $\pi r^2$.
$\therefore \text{Area} = \pi \left( \frac{a}{2} \right)^2 = \pi \left( \frac{a^2}{4} \right) = \frac{\pi a^2}{4} \, cm^2$.
Since $\frac{\pi a^2}{4} \neq \pi a^2$,the given statement is false.