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Look at this square divided into four pieces: two identical triangles and two identical trapezia.

The edge of length 3 from each triangle matches with the edge of length 3 from a trapezium so that the four pieces from the square now occupy a rectangular space.

The square had side length 8 and area 64, but the area of the rectangle is 65 (13 by 5), how can the area have changed ?

And when you know what's happened, can you find any other similar problems?



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