To find the area of a sector of a circle, you can use the formula:
\[ \text{Area of the sector} = \frac{\theta}{360} \times \pi r^2 \]
where:
- \( \theta \) is the angle in degrees,
- \( r \) is the radius of the circle.
In this case, \( \theta = 75 \) degrees and \( r = 4 \) feet.
Plugging in the values:
\[ \text{Area of the sector} = \frac{75}{360} \times \pi \times (4)^2 \]
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
So now we have:
\[ \text{Area of the sector} = \frac{75}{360} \times \pi \times 16 \]
Now simplify \( \frac{75}{360} \):
\[ \frac{75}{360} = \frac{75 \div 15}{360 \div 15} = \frac{5}{24} \]
Thus, the area becomes:
\[ \text{Area of the sector} = \frac{5}{24} \times \pi \times 16 \]
Now multiply \( \frac{5}{24} \) by 16:
\[ \frac{5 \times 16}{24} = \frac{80}{24} = \frac{10}{3} \]
Now we can finalize the area of the sector:
\[ \text{Area of the sector} = \frac{10}{3} \pi \text{ square feet} \]
So, the area of the sector is:
\[ \frac{10}{3} \pi \text{ square feet} \]