Geometric Fallacy and the Golden Ratio

The squares have each been cut into 4 pieces. The top square was cut using consecutive Fibonacci numbers, while the bottom was cut using consecutive numbers in the Golden Sequence. Use the mouse to move the pieces carefully into position in their corresponding rectangles. Take care in postioning the peices and then use the zoom tools to investigate the rectangles. Show or calculate the areas of the squares and rectangles.

How can Rectangle 1 have one less unit than Square 1? Do Square 2 and Rectangle 2 have different areas?