Answer:
The area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]Explanation:
The Area of a sector can be calculated using the formula;
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Where:
A = area of the sector
Angle theta = the angle bounding the sector
r = radius
Given:
[tex]\begin{gathered} \theta=102^0 \\ r=\frac{\text{diameter}}{\text{2}}=\frac{12m}{2}=6m \\ r=6m \end{gathered}[/tex]substituting the given values, we have;
[tex]\begin{gathered} A=\frac{102}{360}\times\pi(6^2) \\ A=10.2\pi m^2 \\ A=32.04m^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]
