Solution
The diagram below will be of help
Note: Area of a Sector Formula
[tex]Area=\frac{\theta}{360}\times\pi r^2[/tex]
Here
[tex]\begin{gathered} r=15 \\ \theta=55^{\circ} \end{gathered}[/tex]
Substituting the parameters
[tex]\begin{gathered} Area=\frac{\theta}{360}\pi r^{2} \\ Area=\frac{55}{360}\times\pi\times15^2 \\ Area=\frac{275}{8}\pi \end{gathered}[/tex]
There are two shaded portion (with the same Area)
Therefore, the area will be
[tex]\begin{gathered} Area=2\times\frac{275}{8}\pi \\ Area=\frac{275}{4}\pi \\ Area=215.9844949 \\ Area=215.98\text{ square unit \lparen to the nearest hundredth\rparen} \end{gathered}[/tex]
The answer is
[tex]\begin{equation*} 215.98\text{ square unit \lparen to the nearest hundredth\rparen} \end{equation*}[/tex]
