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

a. when the plane is parallel to the base of the prism

b. when the plane is perpendicular to the base and contains two edges of the prism

c. when the plane is perpendicular to the base and contains one edge of the prism

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

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.