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The square below has side length 8 and area 64, but the area of the rectangle is 65 (13 by 5). 

It seems that the same four pieces can make two shapes with different areas!

Can you explain where the extra area comes from?



(You might like to try cutting out the shapes from a piece of paper.)



Here are some questions you might like to consider:

Can other squares be split up and rearranged to make rectangles with a different area?

Are there other square/rectangle pairs where the areas differ by 1 square unit?

Is there a pattern in the sizes of squares that can be arranged in this way?