POTW #3 Answer and Explanation

The problem is actually a lot easier than you think, you just need the right way to look at it. Notice that the triangle's hypotenuses (is that the plural for hypotenuse?) have different slopes. In the original picture, the slope of the upper triangle is steeper than the lower one. Because of this, the hypotenuse bends slightly inward, making the area smaller than it appears. In the rearranged triangle, the the triangles switch, so the lower triangle is the one with the steeper slope and the upper one has the more level slope. This makes the hypotenuse slightly outward, which makes the area of the area of the triangle slightly larger than it seems. Since the rearranged triangle is exactly one unit bigger than the original triangle. Therefore, there is a hole of one unit!


By the way, the source of this puzzle was Exidor's Logic Puzzle Place, but you will probably find it in many, many other places too.