A regular pentagon has an apothem of 3.2 m and an area of 37.2m ^ 2 What is the length of one side of the pentagon?
(1 point)
A.3.96 m
B. 465 m
C.11875 m
D.23.75 m
The area (A) of a regular pentagon can be calculated using the formula:
\[ A = \frac{1}{2} \cdot P \cdot a \]
where P is the perimeter of the pentagon and a is the apothem.
Given the area A = 37.2 m^2 and apothem a = 3.2 m, we can rearrange the formula to solve for the perimeter P:
\[ P = \frac{2A}{a} \]
Plugging in the values, we have:
\[ P = \frac{2 \cdot 37.2 \text{ m}^2}{3.2 \text{ m}} \]
\[ P = \frac{74.4 \text{ m}^2}{3.2 \text{ m}} \]
\[ P = 23.25 \text{ m} \]
Since the pentagon is regular, it has five equal sides. Therefore, we can find the length of one side (s) by dividing the perimeter by the number of sides (5):
\[ s = \frac{P}{5} \]
\[ s = \frac{23.25 \text{ m}}{5} \]
\[ s = 4.65 \text{ m} \]
The closest match to the choices you've provided is:
B. 4.65 m
However, this is not exactly one of the choices listed. It seems there might be a typo or a misprint in your options. The correct answer which is not listed in your choices would be 4.65 m for the length of one side of the pentagon.