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 given by: Area = (apothem * perimeter)/2
Given that the apothem is 3.2 m and the area is 37.2 m², we can rearrange the formula to solve for the perimeter.
Perimeter = (2 * Area) / apothem
Perimeter = (2 * 37.2) / 3.2
Perimeter = 74.4 / 3.2
Perimeter = 23.25 m
Since a regular pentagon has 5 equal sides, the length of one side of the pentagon is given by:
Length of one side = Perimeter / 5
Length of one side = 23.25 / 5
Length of one side = 4.65 m
Therefore, the length of one side of the pentagon is 4.65 m.