Answer
The area of given figure is\[257.1\text{ c}{{\text{m}}^{2}}\].
Work Step by Step
Area of given figure will be calculated by computed the area of the square and area of those 4 semicircles given in the figure and then adding the area of that square and 4 semicircles.
The area is expressed as the space enclosed between closed figures to the extent of a two-dimensional figure. According to the formula, compute the area of the figure as shown below:
\[\begin{align}
& \text{Area of square}=\text{Side}\times \text{Side} \\
& =\text{10 cm}\times 10\text{ cm} \\
& =100\text{ c}{{\text{m}}^{2}}
\end{align}\]
Compute the area of 4 Semicircles as mentioned below:
$\begin{align}
& \text{Area of 4 semicircle}=\frac{1}{2}\times \pi \times {{r}^{2}}\times 4 \\
& =\frac{1}{2}\times \pi \times {{\left( 5 \right)}^{2}}\times 4 \\
& =50\pi \text{ c}{{\text{m}}^{2}} \\
& =157.1\text{ c}{{\text{m}}^{2}}
\end{align}$
Compute the area of the given figure as mentioned below:
$\begin{align}
& \text{Area of given figure}=\text{Area of square + Area of 4 semicircles} \\
& =\text{100 c}{{\text{m}}^{2}}\text{+157}\text{.1 c}{{\text{m}}^{2}} \\
& =257.1\text{ c}{{\text{m}}^{2}}
\end{align}$
Hence, the area of given figure is\[257.1\text{ c}{{\text{m}}^{2}}\].
