So, uh... Hmm... Any idea how this works?
 

thats why i always fail at IQ tests...

If the triangle is 5 units by 13 units the overall area is 32.5 units. The hypotenuse does not intersect the unit by unit grid exactly, and when the red and green triangles are switched the areas are not the inverse of each other. the yellow area is also not exactly the same in both as it's upper left corner is truncated slightly along the hypotenuse in one. Drawing the triangles accurately (on graph paper or in CAD) will show that the differences between the colored areas area exactly a single unit.

yes 2+3+5

that .5 thing really fucks with your head doesnt it?

The two triangles have a slightly different slope. One is more steep than the other.

I can SEE why its different and it makes perfect sense in my head, but I could never explain it using the proper terms.

That is why everyone, including psychiatrists say I am smart, but I graduated high school with only a 1.16 GPA.

convex and concave
 

Look at the conglomerates at any point on the top; the height is correspondingly lower on the triangle with no "hole". The first triangle has an angle that is less than 180 and the second has a "bulge" or an angle that is greater than 180. The difference in appparent area is contained within that discrepancy.

Correct...was going to post this. It tricks the eye at first but not if you look close enough to see the slight changes in the perimeter.