Question

type the correct answer in the box. use numerals instead of words. a plane intersects a prism to form a cross - section that is a polygon with five sides. the minimum number of sides that the polygon at the base of the prism must have is

Explanation:

Step1: Understand cross - section concept

A cross - section of a prism is formed by the intersection of a plane and the prism. Each intersection of the plane with a face of the prism creates a side of the polygon cross - section.

Step2: Consider the minimum case

To form a pentagonal (five - sided) cross - section, the plane must intersect at least 5 faces of the prism. The base of the prism is part of these intersections. The minimum number of sides of the polygon at the base of the prism for a plane to be able to form a five - sided cross - section is 3. Because if the base has 3 sides (a triangular base prism), and the plane intersects 2 non - base faces along with the 3 base - intersecting lines, a pentagonal cross - section can be formed.

Answer:

3