Answer
$1116.1$ m$^{2}$
Work Step by Step
Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$.
Step 2: Substituting the values provided by the question into the formula, $A=\frac{1}{2}(29.2)^{2}(\frac{5\pi}{6})$
Step 3: $A=\frac{1}{2}\times(\frac{292}{10})^{2}\times(\frac{5\pi}{6})$
Step 4: $A=\frac{1}{2}\times(\frac{85264}{100})\times(\frac{5\pi}{6})$
Step 5: $A=\frac{5329\pi}{15}=1116.1$ m$^{2}$
