Question

The radius of a regular octagon is 10 centimeters. Identify the calculation that should be used to find the apothem.(1 point)
Responses

a=10cos(22.5°)
a equals 10 cosine left parenthesis 22.5 degrees right parenthesis

a=10sin(22.5°)
a equals Start Fraction 10 over sine 22.5 left parenthesis 22.5 degrees right parenthesis End Fraction

a=10cos(22.5°)
a equals Start Fraction 10 over cosine 22.5 left parenthesis 22.5 degrees right parenthesis End Fraction

a=10sin(22.5°)
a equals 10 sine left parenthesis 22.5 degrees right parenthesis

Answer 1

To find the apothem (a) of a regular octagon given the radius (R) of 10 centimeters, you can use the formula:

\[
a = R \cdot \cos\left(\frac{360°}{2n}\right)
\]

where \( n \) is the number of sides of the polygon (for an octagon, \( n = 8 \)). Thus,

\[
\frac{360°}{2 \cdot 8} = 22.5°
\]

So, the formula becomes:

\[
a = 10 \cdot \cos(22.5°)
\]

Thus, the correct calculation to find the apothem is:

**a = 10 cos(22.5°)**

So, the response you are looking for is:

**a = 10 cos(22.5°)**.