Question

A regular octagon has an apothem of 11.6 inches and a perimeter of 87.2

inches. What is the area of the octagon? *
505.76
1011.52
98.80
2023.04

Answer 1

The area of the octagon is 505.76
`inches^(2)`

Explanation:

In this question, we are tasked with calculating the area of as regular octagon given the lengthy of its apothem ans its perimeter

Mathematically, the area of a regular octagon with an apothem can be calculated as follows

Area = 1/2 × apothem × perimeter

From the question, we can identify the length of the apothem as 11.6 inches and the perimeter of the octagon as 87.2 inches

Now, we plug these values

Area = 1/2 × 11.6 × 87.2 = 505.76
`inches^(2)`