Question

Find the area of the shaded region in the figure given below, if ABCD is a square of side 14 $cm$ and APD and BPC are semicircles.
(Take $\pi =\frac{22}{7}$)

• A. 45 $c{m}^2$
• B. 42 $c{m}^2$
• C. 60 $c{m}^2$
• D. 35 $c{m}^2$

Answer 1

The correct option is B

42 $c{m}^2$

Area of a circle
$=\pi r^2$

From Figure, the diameter of circle is 14 cm. Two semi-circles make one full circle.

$\therefore$ The area of one full circle is
$=\frac{22}{7}\times 7^2=154c{m}^2$

The total area of square
$={14}^2=196c{m}^2$

The area of shaded portion = [Area of square- Area of full circle]
= 196 - 154 = $42c{m}^2$.
Hence, area of shaded region
$=42c{m}^2$