This is going to be a pretty quilt!
If my calculations are correct, a hexagon 6" side-to-side will be 6.93" point-to-point. The formula is:
(side-to-side) x 1.155 = (point-to-point)
Yes, you will need 2 triangles for every hexagon (plus or minus a handful, depending what you do at the edges).
If you want more explanation of my formula, I can do that; I just didn't want to clutter this up with triangles and the square root of 3 and whatnot if you don't want it.
Good luck!