State, the number of faces, number of vertices and number of edges of:
(a) pentagonal pyramid
(b) a hexagonal prism

Answer

To solve the question regarding the number of faces, vertices, and edges of a pentagonal pyramid and a hexagonal prism, we will break down each shape step by step.

### (a) Pentagonal Pyramid

1. **Identify the Faces:**
- A pentagonal pyramid consists of a pentagonal base and 5 triangular lateral faces that connect the base to the apex (top point).
- **Counting the Faces:**
- 1 pentagonal base + 5 triangular faces = 6 faces.

**Total Faces: 6**

2. **Identify the Vertices:**
- The pentagonal base has 5 vertices, and there is 1 additional vertex at the apex.
- **Counting the Vertices:**
- 5 vertices (from the base) + 1 vertex (apex) = 6 vertices.

**Total Vertices: 6**

3. **Identify the Edges:**
- The edges consist of the edges of the pentagonal base and the edges connecting the apex to each vertex of the base.
- **Counting the Edges:**
- 5 edges (from the base) + 5 edges (connecting apex to each vertex) = 10 edges.

**Total Edges: 10**

### Summary for Pentagonal Pyramid:
- Faces: 6
- Vertices: 6
- Edges: 10

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### (b) Hexagonal Prism

1. **Identify the Faces:**
- A hexagonal prism has two hexagonal bases (top and bottom) and 6 rectangular lateral faces connecting the corresponding edges of the hexagons.
- **Counting the Faces:**
- 2 hexagonal bases + 6 rectangular faces = 8 faces.

**Total Faces: 8**

2. **Identify the Vertices:**
- Each hexagonal base has 6 vertices, and since there are two bases, we have a total of 12 vertices.
- **Counting the Vertices:**
- 6 vertices (top base) + 6 vertices (bottom base) = 12 vertices.

**Total Vertices: 12**

3. **Identify the Edges:**
- The edges consist of the edges of the two hexagonal bases and the edges connecting the corresponding vertices of the bases.
- **Counting the Edges:**
- 6 edges (from the top hexagon) + 6 edges (from the bottom hexagon) + 6 vertical edges (connecting the bases) = 18 edges.

**Total Edges: 18**

### Summary for Hexagonal Prism:
- Faces: 8
- Vertices: 12
- Edges: 18

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### Final Summary:
- **Pentagonal Pyramid:**
- Faces: 6
- Vertices: 6
- Edges: 10

- **Hexagonal Prism:**
- Faces: 8
- Vertices: 12
- Edges: 18

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