Question

A prism whose base is a 9-sided polygon is intersected by a plane. In which case could the cross section be a 10-sided polygon?

Answer 1

D.when the plane makes a narrow angle with the base

Answer 2

The correct answer is:

D) when the plane makes a narrow angle with the base.

Explanation:

If a cross section of a prism is taken parallel to the base, the cross section will be the same shape as the base.  In this case, it will be a 9 sided polygon.

If a cross section of a prism is taken perpendicular to the base, the cross section will be a rectangle, no matter how many edges the cross section goes through.

The only way to get a cross section with more sides than the original figure is to take a slant cross section, or one with an angle other than 90° or 180° to the base.  This makes D our only option.