Question

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

Answer 1

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.