The Solution to the Disappearing Square Puzzle

Once I figured this thing out, I decided that I would post the solution to this puzzle.
(I was always looking for the solution online, but it was difficult to find this solution.)  

The purpose of the puzzle is to illustrate area.  When you work out the two solutions to the puzzle, it seems as if some of the area goes missing. 
On the front of the box it is stated in this way,
 "Can you fit all the pieces in place? Can you re-build the puzzle to fill the same space by removing one square? It's not impossible!"

First Solution:

Second Solution:
(Note the narrow gap at the top of the puzzle has the
same area as the green square, which is now 
sitting on the outside of the puzzle.)

Box Cover: