What will be the area of a semi-circle whose perimeter is 36 cm ?

A. 154 cm²

B. 168 cm²

C. 308 cm²

D. Data inadequate

E. None of these

Answer: Option E

Solution(By Examveda Team)

Given :
$$\eqalign{ & \pi R + 2R = 36 \cr & \Leftrightarrow \left( {\pi + 2} \right)R = 36 \cr & \Leftrightarrow R = \frac{{36}}{{\left( {\frac{{22}}{7} + 2} \right)}}cm \cr & \Leftrightarrow R = 7\,cm \cr} $$
Required area :
$$\eqalign{ & = \frac{{\pi {R^2}}}{2} \cr & = \left( {\frac{{22}}{7} \times \frac{{7 \times 7}}{2}} \right)c{m^2} \cr & = 77\,c{m^2} \cr} $$