Answer
$114.0$ cm$^{2}$
Work Step by Step
First converting $81^{\circ}$ to radians:
$81^{\circ}=81(\frac{\pi}{180})=\frac{9\pi}{20}$ radians
The formula for the area of a sector of a circle having radius $r$ and central angle $\theta$ is $A=\frac{1}{2}r^{2}\theta$.
Substituting the values of $r$ and $\theta$ into the formula:
$A=\frac{1}{2}(12.7)^{2}(\frac{9\pi}{20})$
Solving through a calculator:
$A=\frac{1}{2}(12.7)^{2}(\frac{9\pi}{20})\approx114.0$ cm$^{2}$
