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# There is a square with one side being 4 units long. Another square is constructed by connecting the midpoints of the sides of the first square. Another square is constructed by connecting the midpoints of the sides of the second square, and again with this one, and again with all other squares generated. There will be an infinite number of squares. What is their combined area?

Question #57972. Asked by ogicu8abruok. (Jun 26 05 5:58 PM)

shawn888

32 sq. units. It is a case of infinite series addition.

 Jun 26 05, 7:11 PM
gmackematix

In fact if you take the second, fourth, sixth, etc. squares in this series and cut each of them into four right triangles but leave the first, third, fifth, etc. squares in tact, then all the pieces can be rearranged as an infinite piece jigsaw to fit into a 4 by 8 rectangle.

 Jun 26 05, 7:27 PM

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