Checkerboard Paradox

Cut a checkerboard above along the diagonal shown in the first illustration. Then shift part B downward and snip off the projecting triangle at the upper right corner and fit it into the triangular space at the lower left, to give the second illustration.

The first checkerboard is 8x8, with an area of 64. But the second figure is a 7x9 rectangle (area = 63). What happened to the missing square?