To find the area of a regular octagon with an apothem of 10 cm and a side length of 8.3 cm, follow these steps:
1. Determine the number of sides:
An octagon has 8 sides.
2. Calculate the perimeter of the octagon:
The perimeter [tex]\(P\)[/tex] of a regular octagon can be found by multiplying the side length by the number of sides.
[tex]\[
P = \text{Side length} \times \text{Number of sides}
\][/tex]
Given the side length is 8.3 cm and there are 8 sides:
[tex]\[
P = 8.3 \, \text{cm} \times 8 = 66.4 \, \text{cm}
\][/tex]
3. Use the formula for the area of a regular polygon:
The area [tex]\(A\)[/tex] of a regular polygon can be found using the formula:
[tex]\[
A = \frac{1}{2} \times P \times \text{Apothem}
\][/tex]
Here, the perimeter [tex]\(P\)[/tex] is 66.4 cm and the apothem is 10 cm. Substitute these values into the formula:
[tex]\[
A = \frac{1}{2} \times 66.4 \, \text{cm} \times 10 \, \text{cm}
\][/tex]
Simplify the expression:
[tex]\[
A = \frac{1}{2} \times 664 \, \text{cm}^2 = 332.0 \, \text{cm}^2
\][/tex]
Therefore, the area of the regular octagon is [tex]\( 332.0 \)[/tex] square centimeters.
