Number of vertices of a triangular prism is ______ the number of vertices of a square pyramid.

Options

A. Always less than
B. Always greater than
C. Always equal to
D. Sometimes less & sometimes greater

Answer

To solve the question, we need to determine the number of vertices in both a triangular prism and a square pyramid, and then compare them.

### Step-by-Step Solution:

1. **Identify the shape of the triangular prism**:
- A triangular prism has two triangular bases and three rectangular lateral faces.

2. **Count the vertices of the triangular prism**:
- Each triangular base has 3 vertices. Since there are two triangular bases, we have:
- \(3 \text{ (vertices from the first triangle)} + 3 \text{ (vertices from the second triangle)} = 6 \text{ vertices}\).

3. **Identify the shape of the square pyramid**:
- A square pyramid has a square base and four triangular lateral faces that meet at a single apex point.

4. **Count the vertices of the square pyramid**:
- The square base has 4 vertices, and there is 1 apex point at the top. Therefore, we have:
- \(4 \text{ (vertices from the square base)} + 1 \text{ (apex point)} = 5 \text{ vertices}\).

5. **Compare the number of vertices**:
- We found that the triangular prism has 6 vertices and the square pyramid has 5 vertices.
- Thus, we can conclude that the number of vertices of a triangular prism is greater than the number of vertices of a square pyramid.

### Final Answer:
The number of vertices of a triangular prism is **greater than** the number of vertices of a square pyramid.