Question

Find the area of the shaded region in figure. Where ABCD is a square of side $10cm$. (Use $\pi =3.14$)

• A. $32c{m}^2$
• B. $41c{m}^2$
• C. $49c{m}^2$
• D. $57c{m}^2$

Answer 1

The correct option is D $57c{m}^2$

Area of square ABCD$=10\times 10=100c{m}^2$

Area of region $R_1+$ Area of region $R_3$

$=$Area of square-Area of two semicircles of radius $5$cm

$=100-2\left[\frac{1}{2}\pi \right(5{)}^2]=100-25\pi$

Area of region $R_2+$ Area of region $R_4$

=Area of square -Area of two semicircle of radius $5cm$.

$=100-2\left[\frac{1}{2}\pi \right(5{)}^2]=100-25\pi$

So, Area of the shaded region

$=$Area of square-(Area of region $R_1+$ Area of region $R_2+$ Area of region $R_3+$ Area of region $R_4$)

$=100-(100-25\pi +100-25\pi )$

$=50\pi -100$

$=50\times 3.14-100$

$=57c{m}^2$.