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? (1 point) Responses 3.96 m 3.96 m 4.65 m 4.65 m 11.875 m 11.875 m 23.75 m 23.75 m
The formula to calculate the area of a regular pentagon is (1/2) * Perimeter * Apothem.
Given that the apothem is 3.2 m and the area is 37.2 m², we can plug these values into the formula and rearrange to solve for the perimeter:
37.2 = (1/2) * Perimeter * 3.2
74.4 = Perimeter * 3.2
Perimeter = 74.4 / 3.2
Perimeter = 23.25 m
Since a regular pentagon has 5 equal sides, we divide the perimeter by 5 to find the length of one side:
Side length = Perimeter / 5
Side length = 23.25 / 5
Side length = 4.65 m
Therefore, the length of one side of the pentagon is 4.65 m. The correct answer is 4.65 m.