FOOD for THOUGHT - Explanation

Seems puzzling indeed, as it appears to go against logic!

The ‘apparent’ confusion can be explained easily. Just use a bit of mathematical computation.....

Using a bit of elementary trigonometry, we can see that:

In the Green Triangle the tangent of the smaller angle is 2/5 = 0.4, and for the Red Triangle it is 3/8 = 0.375.  If we check the angular values in the Mathematical Tables for tan, the angles will be seen as 23.58 & 22.02 degrees respectively.

It is therefore obvious that with slightly different slope angles, the combined hypotenuses in the two figures do not result in a straight line!  The upper one is slightly depressed, whilst in the lower one it is slightly elevated at the junction point! This makes the total areas of the two images being different, and resulting in the extra square for the latter case!