I obviously have to find some tougher puzzles!
Just curious if 1 - 1/2 - 1/6 was just your way of giving the answer of if it is how you solved it. If the latter, how did you come up with 1/6?
The solution I saw noted that the triangles created on the bottom and top sides were similar. Taking the horizontal sides of the triangles as the bases, we see a 2:1 ratio, that also applies to the altitude, so the altitude of the larger of the triangles is 2/3 times the base.
Area of triangle = 1/2 * base * altitude
= 1/2 * base * 2/3 * base
= 1/3 * base^2