Discussion
If F, V and E are respectively the number of faces, vertices and edges of a triangular prism, then which of the following statements is true ?
Answer: B
The true statement is 2F + 3V - 2E = 10.
A triangular prism has 5 faces (2 triangles and 3 rectangles), 6 vertices and 9 edges. Substituting:
\[ \begin{aligned} 4F + 2V - 3E &= 20 + 12 - 27 = 5 \\ 2F + 3V - 2E &= 10 + 18 - 18 = 10 \\ 2F + 4V - 3E &= 10 + 24 - 27 = 7 \\ 3F + 2V - 2E &= 15 + 12 - 18 = 9 \end{aligned} \]
Only the second equation holds. A quick check on the counts is Euler's formula, F + V - E = 5 + 6 - 9 = 2.
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