SOLUTION: An 8-sided regular polygon (regular octagon) is inscribed in a circle whose radius is 8 inches. Find the area of the polygon. I know to find the area of an octagon, I need to f

Question 1071593: An 8-sided regular polygon (regular octagon) is inscribed in a circle whose radius is 8 inches. Find the area of the polygon.
I know to find the area of an octagon, I need to find the length of a single side of the octagon. I read a lesson created by the Algebra.com tutor ikleyn, on how to find the length of a side of an octagon inscribed in a circle via the circle's radius, but did not quite understand it. Any help solving this problem would be awesome. Thanks!
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This octagon is made of 8 isosceles triangles each of two sides 8 inches and the tip angle of 45 degrees. This makes the other two angles 67.5 degrees each. You can use Law of Cosines to find the length of the side opposite of the tip angle.
Note that the tip angle between each of the two equal sides of the triangle is also a central angle of the circle.

Two sides known, 8 and 8; third side to be found, s;

-
not absolutely the only way
RELATED QUESTIONS
A regular octagon is inscribed in a circle of radius. Find the perimeter of the... (answered by longjonsilver)

A regular 30-sided polygon is inscribed in a circle with a radius of 8. Use the law of... (answered by jim_thompson5910)

A regular octagon is inscribed in a circle of radius 15.8. Find the perimeter of the... (answered by Earlsdon)

The regular octagon is inscribed in a circle with a radius of 5 inches.Each side of the... (answered by fractalier)

Find the area of a regular octagon inscribed into a circle of radius 1. (answered by Theo)

a regular pentagon I inscribed in a circle whose radius is 9 in. find the area of the... (answered by KMST)

Find the side of a regular octagon inscribed in a circle of radius 19 cm. (answered by It is costly,KMST)

Find the side of a regular octagon inscribed in a circle of radius 10 cm. (answered by Alan3354)

How do you find the area of a regular octagon inscribed in a circle with radius... (answered by Alan3354)