To determine the perimeter of the water wheel, which is shaped like a regular octagon, we need to use the properties of a regular octagon.
An octagon is a polygon with 8 equal sides. The perimeter of a regular polygon is calculated by multiplying the length of one side by the total number of sides.
Let’s denote the length of one side of the octagon as [tex]\( s \)[/tex]. For a regular octagon, the perimeter [tex]\( P \)[/tex] is given by:
[tex]\[ P = 8 \times s \][/tex]
Next, we analyze the answer choices:
- A. 80 ft
- B. [tex]\( 8 \sqrt{10} \)[/tex] ft
- C. [tex]\( \sqrt{10} \)[/tex] ft
- D. 8 ft
Given that the perimeter of the octagon can be directly interpreted from these choices, the valid, straightforward answer is:
[tex]\[ P = 80 \text{ ft} \][/tex]
Thus, after determining that the direct length expression in option A results in a valid perimeter for a regular octagon, we conclude the correct answer:
A. 80 ft
