Question

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

4 cm
4 cm

6 cm
6 cm

83–√
cm
8 Start Root 3 End Root cm

43–√
cm

Answer 1

To find the apothem of a regular hexagon, we can use the formula:

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

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

- The side length \( s = 8 \) cm.
- The number of sides \( n = 6 \).

Substituting these values into the formula:

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

Since \( \tan(\frac{\pi}{6}) = \frac{1}{\sqrt{3}} \), the equation becomes:

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

Thus, the exact measure of the apothem is:

\[
4\sqrt{3} \text{ cm}
\]

The correct response from the options provided is \( 4\sqrt{3} \) cm.