Question
A regular hexagon has side lengths of 8 centimeters. What is the exact measure of its apothem?(1 point) Responses 6 cm 6 cm 4 cm 4 cm 83–√ cm 8 Start Root 3 End Root cm 43–√ cm
Answers
GPT-4o mini
To find the apothem of a regular hexagon, we can use the formula for the apothem \( a \):
\[
a = \frac{s}{2 \tan(\frac{\pi}{n})}
\]
where \( s \) is the side length and \( n \) is the number of sides. For a regular hexagon, \( n = 6 \) and the side length \( s = 8 \) cm.
1. Calculate \( \tan(\frac{\pi}{6}) \):
\[
\tan(\frac{\pi}{6}) = \tan(30^\circ) = \frac{1}{\sqrt{3}}
\]
2. Now substitute \( s \) and \( n \) into the formula for the apothem:
\[
a = \frac{8}{2 \cdot \tan(\frac{\pi}{6})} = \frac{8}{2 \cdot \frac{1}{\sqrt{3}}} = \frac{8 \sqrt{3}}{2} = 4\sqrt{3} \text{ cm}
\]
Thus, the exact measure of the apothem of the hexagon is \( 4\sqrt{3} \) cm.
\[
a = \frac{s}{2 \tan(\frac{\pi}{n})}
\]
where \( s \) is the side length and \( n \) is the number of sides. For a regular hexagon, \( n = 6 \) and the side length \( s = 8 \) cm.
1. Calculate \( \tan(\frac{\pi}{6}) \):
\[
\tan(\frac{\pi}{6}) = \tan(30^\circ) = \frac{1}{\sqrt{3}}
\]
2. Now substitute \( s \) and \( n \) into the formula for the apothem:
\[
a = \frac{8}{2 \cdot \tan(\frac{\pi}{6})} = \frac{8}{2 \cdot \frac{1}{\sqrt{3}}} = \frac{8 \sqrt{3}}{2} = 4\sqrt{3} \text{ cm}
\]
Thus, the exact measure of the apothem of the hexagon is \( 4\sqrt{3} \) cm.