[ecurbh]

OK, there is something hinky going on here...

Area = Base x Height / 2

Overall area of both shapes should be 32.5 (13 x 5 / 2)

Area of the red triangle is 12 (8 x 3 / 2)

Area of the green triangle is 5 (5 x 2 / 2)

Area of the other shapes are 7 and 8...

But 12 + 5 + 7 + 8 = 32!

That missing .5 is the key to this. But that's where I get stuck. My brother is a mathematics professor, I'll have to email this to him.

[Swordmaker]

There is a DOUBLE distraction going on here. First the triangles themselves are not identical in proportion or angles... and second the provided "facts". What facts are those? Why the measuring grid! We assume that each square is the same from left to right... they are not. Each square is subtley smaller as you move from left to right. This distorts the measurements of the adjacent sides of the triangles... and then we use this distorted data in our calculations.

Your calculations are correct... but between the fact that the triangles are not the same... and then the fact that they cheat on the measuring ruler, your .5 difference is increased by another .5 to give the appearance of a 1 unit spurious hole.