Answer
The area of given figure is\[\text{110}\text{.57 in}{{\text{.}}^{2}}\]
Work Step by Step
Area of given figure will be calculated by computing 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. It is required to compute the area of the given figure.
Compute the third side that is perpendicular to the triangle shown in the given figure as mentioned below:
\[\begin{align}
& \text{Perpendicula}{{\text{r}}^{2}}=\text{Hypotenus}{{\text{e}}^{2}}-\text{Bas}{{\text{e}}^{2}} \\
& ={{\left( 15 \right)}^{2}}-{{\left( 9 \right)}^{2}} \\
& =225-81 \\
& =\sqrt{144} \\
& =12\text{ in}.
\end{align}\]
Compute the area of the right triangle as mentioned below:
\[\begin{align}
& \text{Area of right triangle}=\frac{1}{2}\times \text{base}\times \text{height} \\
& =\frac{1}{2}\times 9\times 12 \\
& =54\text{ in}{{.}^{2}}
\end{align}\]
Compute the area of the semicircle as mentioned below:
\[\begin{align}
& \text{Area of semicircle}=\frac{1}{2}\times \pi \times {{r}^{2}} \\
& =\frac{1}{2}\times \pi \times 6\text{ in}\text{.}\times 6\text{ in}\text{.} \\
& =18\pi \text{ i}{{\text{n}}^{2}} \\
& =56.57\text{ in}{{.}^{2}}
\end{align}\]
Compute the area of the given figure as shown below:
\[\begin{align}
& \text{Area of given figure}=\text{Area of semicircle}+\text{Area of right triangle} \\
& =56.57\text{ i}{{\text{n}}^{2}}+\text{54 in}{{\text{.}}^{2}} \\
& =110.57\text{ i}{{\text{n}}^{2}}
\end{align}\]
Hence, the area of given figure calculated using the formula is\[\text{110}\text{.57 in}{{\text{.}}^{2}}\]
