Answer:
8 feet
Step-by-step explanation:
The area (A) of a regular hexagon in terms of its side length (s) is ...
A = (3√3)/2·s^2
Then the side length in terms of the area is ...
s = √(2A/(3√3))
For the given base area, the side length is ...
s = √(2(166.28)/(3√3)) ≈ √64.001 ≈ 8.000 . . . . feet
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To confirm this, we can look a the side length that will give the lateral area we have. The lateral area is the difference between the total area and the base area, so is ...
LA = 401.48 -166.28 = 235.20 . . . . square feet
In terms of slant height (h) and side length (s), this area is ...
LA = 3sh
s = LA/(3h) = (235.20 ft^2)/(3·9.8 ft) = 8 ft
Either way we compute it, we find the side length of the base to be 8 feet.
