Answer
$$A \approx 18151 \space ft^2$$
Work Step by Step
Formula for the area of a circular sector: $$A = \frac 12 r^2 \theta$$
r = radius = 5 m
$\theta = angle = 52 ^o$
- In order to substitute the values into the formula, the angle must be converted from degrees to radians:
$$52^o \times \frac{\pi}{180} = \frac{52 \pi}{180} $$
Substituting the values into the formula: $$A = \frac 12 (200 \space ft)^2(\frac{52 \pi}{180}) \approx 18151 \space ft^2$$