Difference of Squares

If a square is put into the corner of a larger square, the region between them can be split up into two rectangles of the same width. That region can also be split up into two congruent trapezoids. If the inside square is put into the middle of the larger square, the region between them can be split up into four congruent trapezoids.

The area of a trapezoid is , where is the height and and are the lengths of the parallel sides.