Question
The radius of a regular octagon is 10 centimeters. Identify the calculation that should be used to find the apothem.
Answers
GPT-4o mini
To find the apothem of a regular octagon with a given radius (circumradius), we can use the following formula:
\[
\text{Apothem} = \frac{R \cdot \cos\left(\frac{\pi}{n}\right)}{1}
\]
where \( R \) is the radius (circumradius) and \( n \) is the number of sides of the polygon. For an octagon, \( n = 8 \).
Thus, the specific calculation you would use for a regular octagon with a radius of 10 centimeters is:
\[
\text{Apothem} = R \cdot \cos\left(\frac{\pi}{8}\right)
\]
Substituting \( R = 10 \) cm, the calculation becomes:
\[
\text{Apothem} = 10 \cdot \cos\left(\frac{\pi}{8}\right)
\]
This will give you the apothem length of the octagon.
\[
\text{Apothem} = \frac{R \cdot \cos\left(\frac{\pi}{n}\right)}{1}
\]
where \( R \) is the radius (circumradius) and \( n \) is the number of sides of the polygon. For an octagon, \( n = 8 \).
Thus, the specific calculation you would use for a regular octagon with a radius of 10 centimeters is:
\[
\text{Apothem} = R \cdot \cos\left(\frac{\pi}{8}\right)
\]
Substituting \( R = 10 \) cm, the calculation becomes:
\[
\text{Apothem} = 10 \cdot \cos\left(\frac{\pi}{8}\right)
\]
This will give you the apothem length of the octagon.