Question

2 hai says that every net for a prism is made up of exactly six faces. explain why hai’s statement is incorrect.

Explanation:

Step1: Recall prism definition

A prism has two congruent polygonal bases (of \(n\)-sides) and \(n\) rectangular (or parallelogram) lateral faces.

Step2: Analyze face count

For a triangular prism (\(n = 3\)): 2 triangular bases + 3 rectangular lateral faces = \(2 + 3 = 5\) faces (not 6).
For a square prism (cube, \(n = 4\)): 2 square bases + 4 rectangular faces = \(2 + 4 = 6\) faces.
So, prisms with non - quadrilateral bases (e.g., triangular, pentagonal) have face counts \(2 + n\) (\(n
eq4\)) which is not 6.

Answer:

Hai’s statement is incorrect because prisms can have different numbers of faces. A prism has 2 congruent polygonal bases and \(n\) lateral faces (where \(n\) is the number of sides of the base polygon). For example, a triangular prism (base is a triangle, \(n = 3\)) has \(2+3 = 5\) faces (2 triangular bases + 3 rectangular lateral faces), not 6. Only prisms with quadrilateral bases (like a rectangular prism) have \(2 + 4=6\) faces, but not all prisms have quadrilateral bases.