Question

How do you find the approximate area of an octagon given its diameter is 8 inches?

Answer 1

Area of octagon is `45.2544` square inches.

Explanation:

Assuming that octagon is inscribed in a circle it appears as follows:

and we can assume the octagon as divided in `8` isosceles triangles, whose equal sides are each 'half of the diameter' and included angle is `45^o`.

As such each side is `4` inches and area of isosceles triangle is

`1/2xx4xx4xxsin45^o`

= `8xx1/sqrt2=4sqrt2`

Hence area of octagon is `8xx4sqrt2=32xx1.4142=45.2544` square inches.