Is the area of the circle inscribed in a square of side $a \,cm , \pi a^{2}\, cm ^{2}?$ Give reasons for your answer.
Is the area of the circle inscribed in a square of side $a \,cm , \pi a^{2}\, cm ^{2}?$ Give reasons for your answer.
False
Let $ABCD$ 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 $\frac{\pi a^{2}}{4} \,cm ^{2}$
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