Try to do this without any visual aids:
Imagine a perfect cube that is placed on a horizontal surface resting on its point (A), so that the opposite point (B is in the air directly above it. (The long diagonal of this cube (AB) would thus be perpendicular to the surface.)
The cube is then cut in half with a horizontal cut - parallel to the surface it is standing on, at the height equal half the length of AB, resulting in two equal shapes.
What is the cross-section of such a cut?
another way to see that the solution is correct is to realize that because all six sides are geometrically equivalent with respect to the "ground" plane or a plane parallel to this which passes through the top point, if a horizontal cut is made through the midpoint between these two such planes, if the cut passes through one face, it must pass through all six faces. To clarify, three cube faces have one corner on the ground plane, and all have the same angle between them and the ground plane (they are simply rotated 120 degrees). The three remaining faces all have a corner on the top point, and again shar the same defection angle from this plane (again - simply rotations of the same thing). Now if an infinite cut is made PERPENDICULAR to the axis of rotation, each face of the top must be affected identically, and each face of the bottom must be effected identically. Finally the symmetry of the situation shows that the top and bottom pieces are effected identically, concluding the illustration, and showing that the cut must pass through all six faces.
no really...
