Answer
The area of the given figure, according to the variables shown is\[A={{a}^{2}}\left( 4+\pi \right)\].
Work Step by Step
We have to find a formula for the area of the given figure. The figure consist of a rectangle and two semicircles of radius equal to a units, on top of the length of the rectangle. For finding out the formula, we have to add the formulas of the figures that make up this figure, according to the given variables.
As two semicircles are on the length of the rectangle,
The length of the rectangle will be equal to twice the diameter of the semicircle. The breadth of the rectangle is a units. The area will be as follows:
\[\begin{align}
& {{A}_{1}}=4a\times a \\
& =4{{a}^{2}}
\end{align}\]
Area of two semicircles will be equal to the area of a circle with radius a units:
\[{{A}_{2}}=\pi {{a}^{2}}\]
So, the total area of the figure will be as follows:
\[\begin{align}
& A=4{{a}^{2}}+\pi {{a}^{2}} \\
& ={{a}^{2}}\left( 4+\pi \right)
\end{align}\]
Hence, the area of the given figure, according to the variables shown is\[A={{a}^{2}}\left( 4+\pi \right)\].
