To find the area of a regular octagon with a given apothem and side length, we can use the formula:
Area = (Perimeter × Apothem) / 2
Given:
Apothem (a) = 18.3 inches
Side length (s) = 15.2 inches
Number of sides (n) for an octagon = 8
First, we need to calculate the perimeter of the octagon.
Perimeter (P) = Side length (s) × Number of sides (n)
P = 15.2 inches × 8
P = 121.6 inches
Now that we have the perimeter, we can calculate the area.
Area = (Perimeter × Apothem) / 2
Area = (121.6 inches × 18.3 inches) / 2
Area = 2225.28 inches² / 2
Area = 1112.64 inches²
So, the area of the regular octagon is 1112.64 square inches.
