Question

A regular hexagon has side lengths of 8 centimeters. What is the exact measure of its apothem?(1 point)
Responses

6 cm


8√3 cm


4√3 cm


4 cm

Answer 1

The apothem of a regular hexagon can be calculated using the formula:

\[
\text{Apothem} = \frac{s}{2 \tan(\frac{\pi}{n})}
\]

where \( s \) is the length of a side, and \( n \) is the number of sides. For a regular hexagon, \( n = 6 \).

First, we can calculate the apothem using the side length \( s = 8 \) cm:

\[
\text{Apothem} = \frac{8}{2 \tan(\frac{\pi}{6})}
\]

We know that \( \tan(\frac{\pi}{6}) = \frac{1}{\sqrt{3}} \), so we substitute:

\[
\text{Apothem} = \frac{8}{2 \cdot \frac{1}{\sqrt{3}}}
\]
\[
= \frac{8 \sqrt{3}}{2}
\]
\[
= 4 \sqrt{3} \, \text{cm}
\]

Thus, the exact measure of the apothem of the regular hexagon is \( 4\sqrt{3} \) cm. Therefore, the correct response is:

**4√3 cm**.