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To solve this problem for the triangular prism shown:

1. **Vertices**: A triangular prism has two triangular bases, each with 3 vertices. Since these bases are connected by edges, the prism has a total of \(3 + 3 = 6\) vertices.

   **Answer for (a): 6 vertices**

2. **Edges**: Each triangular base has 3 edges, and there are 3 lateral edges connecting the corresponding vertices of the two bases. Therefore, the total number of edges is \(3 + 3 + 3 = 9\) edges.

   **Answer for (b): 9 edges**

3. **Faces**: A triangular prism has 2 triangular bases and 3 rectangular lateral faces connecting the bases. This gives a total of \(2 + 3 = 5\) faces.

   **Answer for (c): 5 faces**

Would you like further details on how these properties relate to other types of prisms or any related topics?

Here are 5 questions to expand your understanding:
1. How do the number of vertices, edges, and faces change for a prism with a square base?
2. Can you apply Euler's formula \( V - E + F = 2 \) to verify these counts for the triangular prism?
3. What is the difference between a triangular prism and a triangular pyramid in terms of vertices, edges, and faces?
4. How would these counts change if we considered a right triangular prism instead?
5. How are the shapes of the lateral faces determined by the shape of the base in a prism?

**Tip:** Remember that for any prism, the number of vertices is twice the number of vertices in the base, as each base contributes equally to the total.

Consider the triangular prism shown.
(a) How many vertices does it have?
(b) How many edges (lateral edges plus base edges) does it have?
(c) How many faces (lateral faces plus bases) does it have?

Learn how to determine the number of vertices, edges, and faces of a triangular prism. This problem introduces concepts in 3D geometry and polyhedra properties, including Euler's formula. Suitable for students in Grades 6-8.

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