Yuck

Time for more brainstrain, and I have a real stormer for you. I first came across this at a friend's house when I was about 15. I never solved it then.

Below are 2 triangles, both 13 squares by 5. Each triangle is made up of 6 different shapes, but as you can see, when you reorder them overall, a mysterious square gap appears. Why?

You can print this puzzle out, and try all the shapes for yourself. It really is not possible. Click on the picture to get a full size image.