Math Puzzle From Comments

Zephir gives us a couple of amusing puzzles in the comments, and asks:

Does knowledge of math help or prohibit us in solving of paradoxes like this one?

One
Two


The answer is of course yes. First a note on the puzzling aspect. In One, we get two versions of a 5x13 triangle on a gridded background. Each version is divided into two triangles (2x5, and 3x8) and two other figures. Even though the identical figures appear to be in each, the second has one empty square, so the total area for the sub figures of the first appears to be 32 and 33 for the second, but that's sort of alright since the big triangle should have area 32.5! So what's happening?

The second puzzle has a somewhat similar theme (you need to look). I will put my answer in the comments, in case people want to try the puzzles before looking.

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