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.
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