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Dec 6, 2013 at 15:20 comment added Olga In the 3-dimensional case: the area of the base is the same, the height is different! So the volumes are different too! Although the projections have the same area! Also, in 2-dimensional case, the area of the triangle and the area of the hexagon are not the same. Just to conclude that the initial question about volumes is also anwered here.
May 15, 2010 at 11:56 vote accept Rob Grey
May 15, 2010 at 7:54 history answered Sergei Ivanov CC BY-SA 2.5