Take a checker board [8 x 8 = 64] and cut carefully from the bottom corner to a point between the top first and second square ...

Wait! ... Save your checker board! ... It is easier to do this with a square sheet of paper .... [Note: If you are using INTERNET EXPLORER, you can actually slide the pieces on your screen. If you are using another browser, you may have to use paper, as the screen sliding will not work.] ... Now slide upwards the triangle that you have just cut ... thus making a rectangle ... with a missing triangle at the top left and with a protruding triangle at the bottom right ... cut the protruding triangle and you will see that it fits in the missing spot. Now you have a rectangle that measures 7 x 9 = 63!!! Where did that darned square go to???
Note: The pieces may not be exact on the screen.