Question

The base of a cube is parallel to the horizon. If the cube is cut by a plane to form a cross section, under what circumstance can the cross section be a non-rectangular parallelogram?

Answer 1

To create a non-rectangular parallelogram, slice with a plane from the top face to the bottom. The slice cannot be parallel to any side of the top face, and the slice must not be vertical. This allows the cut to form no 90° angles. One example is to cut through the top face at a corner and a midpoint of a non-adjacent side, and cut to a different corner and midpoint in the bottom face.

Answer 2

When the plane makes an acute angle to the base and intersects three vertical faces.

Explanation:

The base of a cube is parallel to the horizon

If the cube is cut by a plane to form a cross section, the circumstances under which the cross section will be a non-rectangular parallelogram is-when the plane makes an acute angle to the base and intersects three vertical faces.