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

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Question

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

Answer: Option E
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 :
$$\eqalign{
& = \frac{{\pi {R^2}}}{2} \cr
& = \left( {\frac{{22}}{7} \times \frac{{7 \times 7}}{2}} \right)c{m^2} \cr
& = 77\,c{m^2} \cr} $$

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