I've seen this one before, and I believe the solution is along the lines...
Spoiler:... by virtue of the various building blocks that form the triangle, the edge that forms the hypotenuse of the right triange is not perfectly straight. Rather, it bows in on the top picture and bows out on the bottom, with area in the "missing square" being distributed along the entire length. In other words, the slopes of the green triangle and red triangle are slightly different.
You're exactly right, Mat.
Spoiler:Both diagrams have exactly the same 'covered' area. The slope in picture one *looks* straight, but in reality there's a bend.
------------------ Nothing In Particular
Ding Ding Ding! For the correct answer you get a hot cup of jack squat!!!
Spoiler:You can calculate the clope of the two triangles to see that they are not the same. The green triangle has a rise over run of:
2/5 = 0.4
The Red Triangle has a rise over run of:
3/8 = .375
Since they do not have the same slope the triangle bows out on the bottom triangle and bows in on the top triangle making up for lost square!
-Jin My Theater