Question

A square of diagonal 8 cm is inscribed in a circle. Then the area of the shaded region is

• A. $(16\pi +32)c{m}^2$
• B. $(32\pi -16)c{m}^2$
• C. $(32\pi +16)c{m}^2$
• D. $(16\pi -32)c{m}^2$

Answer 1

The correct option is D $(16\pi -32)c{m}^2$

Given: A square of diagonal $d=8cm$ has been inscribed in a circle as shown in the figure.

To find the area of shaded region in the figure

The square has been inscribed in the circle.

$\therefore$ All the four corners of the square lie on the circle

$\therefore$ The diameter $D$ of the circle circumscribing the square

$=$ diagonal $d$ of the square. i.e $D=d=8cm.$

$\therefore$ area of circle $=\pi \times (4{)}^2=16\pi {cm}^2$

Also area of square $=\frac{{diagonal}^2}{2}=\frac{8^2}{2}{cm}^2=32{cm}^2.$

Now from the figure, it is clear that

area of shaded region $=$ area of circle $-$ area of square

$⟹$ area of shaded region $=16\pi {cm}^2-32{cm}^2=(16\pi -32){cm}^2.$

Hence, option D is correct.