Question

Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

• A. $82c{m}^2$
• B. $36c{m}^2$
• C. $42c{m}^2$
• D. $54c{m}^2$

Answer 1

The correct option is C

$42c{m}^2$

There are two semicircles in the figure.
Side of the square = 14 cm
Diameter of the semicircle = 14 cm
$\therefore$ Radius of the semicircle = 7 cm
Area of the square $=14\times 14=196c{m}^2$
Area of the semicircle $=\frac{\left(\pi R^2\right)}{2}$
$=\frac{(\frac{22}{7}\times 7\times 7)}{2}c{m}^2=77c{m}^2$
Area of two semicircles
$=2\times 77c{m}^2=154c{m}^2$
Area of the shaded region
= Area of the square - Area of the semicircles
$=196c{m}^2-154c{m}^2=42c{m}^2$