Explanation
$${\textbf{Hint:Recall the Area of Circle and Semicircle}}$$
$${\textbf{Step -1: Find the area of the semicircle.}}$$
$${\text{From the figure we can observe that both the semicircles have same radius}}{\text{.}}$$
$${\text{i.e}}{\text{.}}$$$$r = 4cm$$
$${\text{Area of semicircle}}$$ $$ = \frac{{\pi {r^2}}}{2}$$
$$\Rightarrow $$ $${\text{Area of semicircle}}$$ $$ = \frac{{\pi {{\left( 4 \right)}^2}}}{2}$$
$$\Rightarrow $$ $${\text{Area of semicircle}}$$ $$ = \frac{{3.14 \times 16}}{2} = 25.12c{m^2}$$
$${\text{Since, both the semicircles are same}}{\text{.}}$$
$$\therefore $$ $${\text{Area of not shaded part}}$$ $$ = 2 \times $$ $$\left( {{\text{Area of semicircle}}} \right)$$
$$ = 2 \times 25.12c{m^2}$$
$$ = 50.24c{m^2}$$
$$\textbf{Step -2: Find area of circle having radius as }$$$$\mathbf{ 8 cm.}$$
$${\text{Area of circle }}\left( {\text{A}} \right)$$ $$ = \pi {r^2}$$
$$ \Rightarrow A = 3.14 \times 8 \times 8$$
$$ \Rightarrow A = 200.96c{m^2}$$
$${\textbf{Step -3: Find area of shaded part.}}$$
$${\text{Area of shaded part}}$$$$ = $$$$\left( {{\text{Area of circle}}} \right) - \left( {{\text{Area of two semicircles}}} \right)$$
$$ \Rightarrow {\text{Area of shaded part}}$$ $$ = 200.96 - 50.24$$
$$ \Rightarrow {\text{Area of shaded part}}$$ $$ = 150.72c{m^2}$$
$${\textbf{ Hence, the area of shaded portion is }}$$$$\mathbf {150.72 sq.cm} \mathbf .$$
$$\textbf{So, the correct option is A.}$$
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