Question

Question 2
In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Answer 1

Let the side of square be a and the radius of circle be r

Given: length of diagonal of square = 8cm

$\Rightarrow a\sqrt{2}=8$

$\Rightarrow a=4\sqrt{2}cm$

$\Rightarrow$ Area of square = Side${}^2$ = $(4\sqrt{2}{)}^2$ = 32 cm${}^2$

Now, Diagonal of a square = Diameter of a circle

$\Rightarrow$ Diameter of circle = 8

$\Rightarrow$ Radius of circle$=r=\frac{Diameter}{2}$

$\Rightarrow r=\frac{8}{2}=4cm$

$\therefore$ Area of circle $=\pi r^2=\pi (4{)}^2$

$=16\pi \times c{m}^2$

So, the area of the shaded region = Area of circle – Area of square

$=(16\pi -32)c{m}^2$

Hence, the required area of the shaded region $=(16\pi -32)c{m}^2$