Question

The perimeter of a semicircle on diameter AB is $(3.5\pi +7)cm$. The area enclosed by the semicircle is

• A. $77c{m}^2$
• B. $\frac{77}{2}c{m}^2$
• C. $\frac{7\pi }{4}c{m}^2$
• D. $\frac{49\pi }{8}c{m}^2$

Answer 1

The correct option is D $\frac{49\pi }{8}c{m}^2$

Perimeter of semicircle $=\pi r+2r=3.5\pi +7$ (given)
$\Rightarrow r=\frac{7}{2}$
$Area=\frac{1}{2}\pi r^2=\frac{\pi }{2}\times \frac{7}{2}\times \frac{7}{2}=\frac{49\pi }{8}c{m}^2$