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?

The answer is so obviously a square, don't use any equations to try and figure it out. The result leaves two four-sided pyramids, so the cross section (the bases of the pyramids) is a square.

Posted by Mike on 2002-05-10 15:00:13