Answer
The area of the shaded region of the given figure, in terms of \[\pi \] is\[8\pi \text{c}{{\text{m}}^{2}}\].
Work Step by Step
We have to find the area of the shaded region in the given figure. It can be found out by subtracting the area of the two smaller circles, with radius equal to \[2\text{ cm}\],from the area of the bigger circle, that has the radius equal to \[2\times 2=4\text{ cm}\](as the diameter of the smaller circle is equal to the radius of the bigger circle).
According to this formula, the area of the bigger circle, with radius equal to \[4cm\] will be:
\[\begin{align}
& {{A}_{1}}=\pi {{r}^{2}} \\
& =\pi \times \text{4 c}{{\text{m}}^{2}} \\
& =\text{16}\pi \text{ c}{{\text{m}}^{2}}
\end{align}\]
The area of the smaller circle, with radius equal to \[2\text{ cm}\] will be
\[\begin{align}
& {{A}_{2}}=\pi {{r}^{2}} \\
& =\pi \times 2\text{ c}{{\text{m}}^{2}} \\
& =4\pi \text{ c}{{\text{m}}^{2}}
\end{align}\]
Since there are two smaller circles to be subtracted from the bigger circle, the area of the shaded region will be:
\[\begin{align}
& A={{A}_{1}}-2.{{A}_{2}} \\
& =\text{16}\pi -2\times 4\pi \\
& =\text{8}\pi \text{ c}{{\text{m}}^{2}}
\end{align}\]
Hence, the area of the shaded region of the given figure, in terms of \[\pi \] is\[8\pi \text{ c}{{\text{m}}^{2}}\].
