To calculate the area of a sector of a circle, you can use the formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
where \( A \) is the area of the sector, \( \theta \) is the angle in degrees, and \( r \) is the radius.
Given:
- \( \theta = 75^\circ \)
- \( r = 4 \) feet
First, plug the values into the formula:
\[ A = \frac{75}{360} \times \pi (4^2) \]
Calculating \( 4^2 \):
\[ 4^2 = 16 \]
Now, substitute that into the formula:
\[ A = \frac{75}{360} \times \pi \times 16 \]
To simplify \( \frac{75}{360} \):
\[ \frac{75}{360} = \frac{5}{24} \]
Now substitute that back into the area formula:
\[ A = \frac{5}{24} \times \pi \times 16 \]
Calculating \( 5 \times 16 \):
\[ 5 \times 16 = 80 \]
Thus,
\[ A = \frac{80}{24} \pi \]
Now simplify \( \frac{80}{24} \):
\[ \frac{80}{24} = \frac{10}{3} \]
Therefore, the area of the sector is:
\[ A = \frac{10}{3} \pi \text{ ft}^2 \]
Approximating \( A \) with \( \pi \approx 3.14 \):
\[ A \approx \frac{10}{3} \times 3.14 \approx 10.472 \text{ ft}^2 \]
The final answer, including \(\pi\), is:
\[ A = \frac{10}{3} \pi \text{ ft}^2 \quad \text{or approximately } 10.472 \text{ ft}^2 \]
Thus, the correct response is:
A = 10.472 ft².