Didn't you draw a picture? For such problems, drawing the diagram is not only helpful visually, it often can lead to ideas for a proof. Now there are infinitely many equilateral triangles inscribed in a circle of radius 6, same for circumscribed triangles and inscribed hexagons. The areas though are always the same -- needs proof, I guess.

Anyway, here's the "best" figure for proof of your problem:

Unless you know some trigonometry, I don't see how you can give the exact areas, but geometrically you can find the relationships among the 3 areas. Good luck.