Hooper's paradox

Geometry Level 1

An $8 \times 8$ square with area 64 is split into 4 pieces, as shown on the left. Then, the 4 pieces are rearranged to form a $13\times 5$ rectangle whose area is 65.

How did this happen?

Some of the shapes in the rectangle are overlapping in a way that creates the illusion It must be a work of the Illuminati The individual shapes on the left are not the same as those on the right The shapes in the square don't fit up exactly as shown in the rectangle, and their areas differ by 1