Question

A circle of radius $\sqrt{7}$ cm is inscribed in a square. Find the area of the shaded region. $(\text{use}\pi =\frac{22}{7})$

${\text{cm}}^2$

Answer 1

Given, the radius of the circle$\left(r\right)$ is $\sqrt{7}$ cm.

Step 1: Area of the circle $=\pi \times r^2=\frac{22}{7}\times (\sqrt{7}{)}^2(\because \text{given,}\pi =\frac{22}{7})=\frac{22}{7}\times 7=22{\text{cm}}^2$

Step 2:
$\text{Diameter of the circle}=2\times r=2\times \sqrt{7}=2\sqrt{7}\text{cm}$

When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square.

So, the side length of the square$\left(s\right)$ is $2\sqrt{7}\text{cm}$.

$\text{Area of the square}=(s{)}^2=(2\sqrt{7}{)}^2=2^2\times (\sqrt{7}{)}^2=4\times 7=28{\text{cm}}^2$

Step 3: As, the area of the square is a sum of the area of the circle and the area of the shaded region.
$\therefore \text{Area of the shaded region = Area of the square}-\text{Area of the circle}$
$=28-22$
$=6{\text{cm}}^2$