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

When the plane intersects the polygon at any given two adjacent sides of the base. 

Answer 2

when the plane makes a narrow angle with the base.

Explanation:

Given: A prism with a Nonagon as base.

To find: When a cross section be a Decagon.

Nonagon is a polygon with 9 sides

Decagon is a polygon with 10 sides.

1). when a cross section is taken parallel to the base, the cross section will be Nonagon .i.e., it will be a 9 sided polygon.

2).when a cross section is taken perpendicular to the base, the cross section will be a rectangle.

3). when a slant cross section is taken .i.e., one with any angle other than 90° or 180° to the base. It will be a 10-sided polygon.