Final answer:
The question is about finding the area of a sector of a circle with a diameter of 34 feet and an angle of 5π / 8 radians. The first step is to find the radius by halving the diameter, then calculate the area of the full circle, and lastly, multiply the full circle's area by the fraction of the circle that the given angle represents.
Step-by-step explanation:
To find the area of a circle with a given diameter and an angle, you would typically use the formula A = πr² where A is the area and r is the radius. However, since the question mentions an angle, it seems we are being asked to find the area of a sector of a circle, not the entire circle.
Firstly, we need to calculate the radius of the circle. Since the diameter is provided as 34 feet, the radius r is half of that, which is 17 feet. Next, we calculate the area of the entire circle using the formula A = πr², which gives us A = 3.14159 × (17 feet)².
Calculating this, we get the full circle's area. However, since we need the area of the sector formed by the angle of 5π / 8 radians, we need to multiply the full circle's area by the fraction of the circle that this angle represents. The full circle is 2π radians, thus, the fraction is (5π / 8) / (2π). Multiplying the circle's full area by this fraction will give us the area of the sector.
Without a calculator for precision, we can only describe the steps here. But it's critical to understand the significance of the given angle to calculate the desired sector area.