Aregular octagon is inscribed in a circle with a radius of 5 feet. what is the area of the octagon

70.58 ft²

Step-by-step explanation:

One pie-shaped sub-area of this octagon has two sides of length 5 ft and a central angle of 360°/8, or 45°.  We need to find the area of one such sub-area and then multiply the result by 8 to find the total area of the octagon.

Picture this pie-shape, this isosceles triangle with two sides of length 5 ft and central angle 45°.  Half of that angle is 22.5°.  Half of the base of this triangle is 5 sin 22.5°, or 1.91; the full base length is twice that, or 3.82.  the height of the triangle is 5 cos 22.5°, or 4.62.

The formula for the area of a triangle is

A = (1/2)(base)(height), which in this case is:

A = (1/2)(3.82 ft)(4.62 ft) = 8.82 ft²

and so the area of the whole octagon is 8(8.82 ft²), or 70.58 ft²