To find the apothem of a regular octagon with a given radius (in this case, 10 cm), you use the formula for the apothem \( a \) in relation to the radius \( r \):
\[ a = r \cdot \cos\left(\frac{\pi}{n}\right) \]
where \( n \) is the number of sides of the polygon.
For a regular octagon, \( n = 8 \), and thus:
\[ a = 10 \cdot \cos\left(\frac{\pi}{8}\right) \]
Since \( \frac{\pi}{8} \) in degrees is equal to \( 22.5^\circ \), we can express the calculation for the apothem as:
\[ a = 10 \cdot \cos(22.5^\circ) \]
Therefore, the correct response is:
a = 10 cos(22.5°)
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