A regular hexagon is inscribed in a circle of radius 25 inches find the length of the sides of the hexagon. A regular hexagon is inscribed in a circle of radius 25 inches find the length of the sides of the hexagon. @Mathematics

Question

jamesj · Answer

The hexagon comprises of six triangles, two sides being radii and the other being the 'external side'.  Making sense?

jamesj · Answer

And each of those triangles is isosceles because the two sides that are radii are of equal length.  But it also turns out that angle between those two sides is 60 degrees.  Hence the other two angles are also 60 degrees.  Therefore each triangle is also equilateral.

anonymous · Answer

so the answer is 25?

jamesj · Answer

Therefore the length of each side is the length of the radius r.

jamesj · Answer

Now there are six sides to a hexagon.  Therefore the perimeter is 6 times the side length ... which is ... what?

jamesj · Answer

Oh wait, the question asks for the length of the sides, so, yes: 25 is the answer.

anonymous · Answer

Awesome, thanks man