Question

Figure consist of four adjacent semicircles of equal radii and two big semicircles having equal radii(14 cm), then find the area of shaded region.

• A. 154 $c{m}^2$
• B. 308 $c{m}^2$
• C. 616 $c{m}^2$
• D. 1232 $c{m}^2$

Answer 1

The correct option is C 616 $c{m}^2$


As figure is symmetric about vertical line
Area of figure(1) = Area of figure(2)
Area of entire fig = 2$\times$Area of figure(1)

Area of figure(1)
= Area of semicircle having diameter AC
- Area of semicircle having diameter AB
+ Area of semicircle having diameter BC

As AB=BC, areas of their semicircle will be same
Hence
Area of figure(1)
= Area of semicircle having diameter AC
= $\frac{1}{2}$$\times$$\pi$$r^2$ = $\frac{1}{2}$$\times$ $\frac{22}{7}$$\times$${14}^2$
= 22$\times$14 = 308 $c{m}^2$

area of entire fig = 2$\times$Area of figure(1)
= 2$\times$308 = 616 $c{m}^2$