To determine the perimeter of a water wheel designed in the shape of a regular octagon, follow these steps:
1. Understand the properties of a regular octagon:
- A regular octagon has eight sides of equal length.
2. Determine the side length of the octagon:
- Let’s assume a hypothetical scenario where the side length of the regular octagon is [tex]\(10\)[/tex] ft.
3. Calculate the perimeter:
- The perimeter ([tex]\(P\)[/tex]) of a regular octagon is given by the formula:
[tex]\[
P = 8 \times \text{side length}
\][/tex]
4. Substitute the side length into the formula:
- Substituting the side length of [tex]\(10\)[/tex] ft, we get:
[tex]\[
P = 8 \times 10 \text{ ft}
\][/tex]
- Simplifying this, the perimeter [tex]\(P\)[/tex] is:
[tex]\[
P = 80 \text{ ft}
\][/tex]
Therefore, the correct answer is:
D. 80 ft
