In the below figure, $ A B C D $ is a rectangle, having $ A B=20 \mathrm{~cm} $ and $ B C=14 \mathrm{~cm} $. Two sectors of $ 180^{\circ} $ have been cut off. Calculate the area of the shadded region."

Given:

\( A B C D \) is a rectangle, having \( A B=20 \mathrm{~cm} \) and \( B C=14 \mathrm{~cm} \). Two sectors of \( 180^{\circ} \) have been cut off.

To do: 

We have to calculate the area of the shaded region.

Solution:

Length of the rectangle $= 20\ cm$

Breadth of the rectangle $= 14\ cm$

This implies,

Area of the rectangle $= 20 \times 14$

$= 280\ cm^2$

Radius of each semicircle $r=\frac{\mathrm{BC}}{2}$

$=\frac{14}{2}$

$=7 \mathrm{~cm}$

This implies,

Area of two semicircles $=2 \times \frac{1}{2} \pi r^{2}$

$=\pi r^{2}$

$=\frac{22}{7} \times 7^2$

$=154 \mathrm{~cm}^{2}$

From the figure,

Area of the shaded region $=$ Area of the rectangle $-$ Area of two semicircles

$=280-154$

$=126 \mathrm{~cm}^{2}$

The area of the shaded region is $126\ cm^2$.