Question:
Is the area of the circle inscribed in a square of side a cm, πa2 cm2 ? Give reasons for your answerin a square of side a cm, πa2 cm2 ? Give reasons for your answer
Solution:
False
Let $A B C D$ be a square of side $a$.
$\therefore$ Diameter of circle $=$ Side of square $=a$
$\therefore \quad$ Radius of circle $=\frac{a}{2}$
$\therefore \quad$ Area of circle $=\pi$ (Radius) $^{2}=\pi\left(\frac{a}{2}\right)^{2}=\frac{\pi a^{2}}{4}$
Hence, area of the circle is $\frac{\pi a^{2}}{4} \mathrm{~cm}^{2}$.