A regular pentagon has an apothem of 3.2 m and an area of 37.2 m². What is the length of one side of the pentagon?
A. 3.96 m
B. 4.65 m
C. 11.875 m
D. 23.75 m
The formula for the area of a regular pentagon is (1/2) × apothem × perimeter. Let's denote the length of one side of the pentagon as x.
First, we can use the given apothem to find the perimeter:
37.2 = (1/2) × 3.2 × perimeter
perimeter = 23.25
Now we can use the perimeter to find x:
x = perimeter/5 = 23.25/5 = 4.65
Therefore, the length of one side of the pentagon is 4.65 m.
The answer is B.