Question

ABCD is a rectangle with AB = 28 cm and BC = 14 cm. Taking DC, BC, and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of shaded region. (Use $\pi$ =$\frac{22}{7}$)

• A. 438 ${cm}^2$
• B. 338 ${cm}^2$
• C. 200 ${cm}^2$
• D. 238 ${cm}^2$

Answer 1

The correct option is D 238 ${cm}^2$

Area of rectangle ABCD = AB $\times$ BC = 28 $\times$ 14 = 392 ${cm}^2$

Area of semicircle = $\frac{1}{2}$ $\times$$\frac{\pi }{4}$ $\times$ $D^2$
Area of semicircle CD
= $\frac{1}{2}$ $\times$$\frac{\pi }{4}$ $\times$ ${CD}^2$

=$\frac{1}{2}$ $\times$$\frac{\pi }{4}$ $\times$ ${28}^2$ [Use $\pi$ = $\frac{22}{7}$]

= 308 ${cm}^2$

As, AD = BC

So,
Area of semicircle of radius BC = Area of Semicircle of radius AD
= $\frac{1}{2}$ $\times$$\frac{\pi }{4}$ $\times$ ${AD}^2$

= $\frac{1}{2}$ $\times$$\frac{\pi }{4}$ $\times$ ${14}^2$ [Use $\pi$ = $\frac{22}{7}$]

= 77 ${cm}^2$

Area of shaded portion = [Area of rectangle ABCD – Area of semicircle of radius CD) + Area of semicircle BC + Area of semicircle AD]

Area of shaded portion
= (392 – 308) +2 $\times$ 77
= 238 ${cm}^2$