Final answer:
To find the perimeter of a regular octagon inscribed in a circle, we need to know the side length of the octagon. Since the circle has a radius of 28.1 centimeters, we can use the formula for the apothem of an octagon to calculate the perimeter.
Step-by-step explanation:
To find the perimeter of a regular octagon inscribed in a circle, we need to know the side length of the octagon. Since the octagon is regular, all sides are equal.
Let's start by computing the apothem of the octagon, which is the distance from the center of the octagon to the midpoint of any side.
Since the circle has a radius of 28.1 centimeters, the apothem will also be 28.1 centimeters.
An octagon has 8 sides, so the perimeter of the octagon will be 8 times the length of one side.
Using the formula for the apothem of an octagon, we have:
Perimeter = 8 x (2 * apothem)
Perimeter = 8 x (2 * 28.1) = 8 x 56.2 = 449.6 centimeters
Therefore, the perimeter of the octagon is approximately 449.6 centimeters when rounded to the nearest tenth.