What is the sum of the number of faces and the number of vertices of an n-gonal prism?
A) 2n
B) n + 2
C) 3n
D) 3n + 2
E) None of the answers is correct.

Question

Quizplus · Accepted Answer

An n-gonal prism has 2n vertices (n vertices on each of the two n-gonal bases) and 3 sets of faces: 2 n-gonal bases and n rectangular side faces, totaling n + n + n = 3n faces. However, the question asks for the sum of the number of faces and vertices, which is 2n (vertices) + 3n (faces) = 5n, not matching any of the provided options directly. The correct interpretation, considering standard geometric formulas, should be 2n (for the vertices on the two bases) + n (for the side faces), giving us 3n. However, this overlooks the additional 2 faces (the bases), leading to the correct total being 3n + 2. My initial explanation mistakenly combined aspects of counting faces and vertices, leading to confusion. The correct answer, focusing on the sum of faces and vertices, indeed aligns with option D, reflecting the accurate count of 2n vertices and n + 2 faces for an n-gonal prism, summing to 3n + 2.

What Is the Sum of the Number of Faces and the Number