Triangle to Square Puzzle

Thanks for giving this a look! I've been trying to find a nice way to break a square up into the seven different triangle types forever. But now that I've found it, it's fallen apart! 1) Can you help me put it back together into a square? 2) Why are the pieces colored the way they are? 3) Can you make any interesting pictures out of the pieces? (Why should those tangrams have all the fun?)