Answer:
To find the length of the sides of the octagon, we can use the formula:
Area = (1/2) × Apothem × Perimeter
Given the following values:
Area = 242 in²
Apothem = 12.1 in
Let's rearrange the formula to solve for the perimeter:
Perimeter = (2 × Area) / (Apothem)
Plugging in the values:
Perimeter = (2 × 242 in²) / (12.1 in)
Perimeter = 484 in² / 12.1 in
Perimeter = 40 in
The perimeter of the octagon is 40 inches. Since an octagon has 8 sides, each side would have a length of:
Length of each side = Perimeter / Number of Sides
Length of each side = 40 in / 8
Length of each side = 5 in
Therefore, the length of each side of the octagon is 5 inches.
Step-by-step explanation: