Thread: Hexagon inscribed in circle gr.10

this is apparantly gr. 10 'challenge 'material which I have no idea how to solve.

If a regular hexagon is inscribed in a circle, and the apothem of the hexagon is 5, find the area between the circle and the hexagon.

I know i have to find the area of the isosoceles triangles formed from the apothem as the height then subtract it from the circle area. How do you find the side of the isocles triangle one can create by forming a line to the adjacent vertex? that's all i am asking, and please tell me if im on the right track to the solution. thanks!!

Originally Posted by Macmade

If a regular hexagon is inscribed in a circle, and the apothem of the hexagon is 5, find the area between the circle and the hexagon.

Have a look at this webpage.
A regular inscribed hexagon creates six sectors.
This case .
From formula (3) you can get the radius R.

This page may also help.