9514 1404 393
Answer:
a = 74 cm
Explanation:
The relationship between the apothem, side length, and area is usually expressed in the formula ...
A = 1/2Pa
where P is the perimeter of the regular polygon. Here, P = 5s, so the area is ...
A = (1/2)(5s)a
Solving for the apothem, a, we have ...
a = 2A/(5s)
a = 2(19887.5 cm^2)/(5(107.5 cm)) = (39775/537.5) cm
a = 74 cm
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Additional comment
The integer result confirms the above approach you're intended to use with this problem.
The apothem can also be found from the side length directly (without regard to the area). In an n-sided regular polygon, ...
a = (s/2)/tan(180°/n)
For s=107.5 and n=5, this is
a = 107.5/(2·tan(36°)) ≈ 73.98
This problem is one of the better ones in that the apothem comes out about the same either way it is calculated. We have seen many (poorly-devised) math problems where using one formula gives vastly different results than those obtained from the other formula.