[Swordmaker]

A Two unit high by five unit long right triangle does not have the same angle at the top angle as a three unit high by eight unit long right angle. The first set up has a subtle but noticeable downward bend along the top side where the two triangles meet. When you reposition the pieces, the bend is reversed, bending upwards, adding area to the over all triangle. This differential is equal to one square unit.

[HairOfTheDog]

There is an optical illusion that would suggest an arc, but there is no arc. I confirm with Photoshop that the hypotenuse is a straight line in both.