Question

Explain why a cross section of a polyhedron does not always match the base of that polyhedron.

Answer 1

Explanation:

If the polyhedron is a prism and the cross sections are parallel to the base, then the cross section will match the base. Under other conditions, the cross section may not match the base.

For example, the first attachment is a figure of a cube. Cross sections are shown that have the shape of a triangle, trapezoid and hexagon. Other cross sections are possible.

A general polyhedron need not be regular and need not have any cross section congruent to the base (except the cross section that is the base). For some polyhedrons, it may be difficult even to identify the base. See the second attachment.