Select the incorrect match of given solids with the product of their number of faces and vertices.

Options

A. Rectangular pyramid - 25
B. Triangular prism - 30
C. Octahedron - 48
D. Triangular pyramid - 18

Answer

To solve the problem of selecting the incorrect match of given solids with the product of their number of faces and vertices, we will analyze each solid step by step.

### Step 1: Rectangular Pyramid
1. **Identify the number of faces**: A rectangular pyramid has 4 triangular faces and 1 rectangular base.
- Total faces (F) = 4 + 1 = 5
2. **Identify the number of vertices**: A rectangular pyramid has 5 vertices (4 at the base and 1 at the apex).
- Total vertices (V) = 5
3. **Calculate the product of faces and vertices**:
- F × V = 5 × 5 = 25

### Step 2: Triangular Prism
1. **Identify the number of faces**: A triangular prism has 2 triangular faces and 3 rectangular faces.
- Total faces (F) = 2 + 3 = 5
2. **Identify the number of vertices**: A triangular prism has 6 vertices (3 at the top triangle and 3 at the bottom triangle).
- Total vertices (V) = 6
3. **Calculate the product of faces and vertices**:
- F × V = 5 × 6 = 30

### Step 3: Octahedron
1. **Identify the number of faces**: An octahedron has 8 triangular faces.
- Total faces (F) = 8
2. **Identify the number of vertices**: An octahedron has 6 vertices.
- Total vertices (V) = 6
3. **Calculate the product of faces and vertices**:
- F × V = 8 × 6 = 48

### Step 4: Triangular Pyramid
1. **Identify the number of faces**: A triangular pyramid has 3 triangular faces and 1 triangular base.
- Total faces (F) = 3 + 1 = 4
2. **Identify the number of vertices**: A triangular pyramid has 4 vertices (3 at the base and 1 at the apex).
- Total vertices (V) = 4
3. **Calculate the product of faces and vertices**:
- F × V = 4 × 4 = 16

### Conclusion
Now we summarize the results:
- Rectangular Pyramid: F × V = 25
- Triangular Prism: F × V = 30
- Octahedron: F × V = 48
- Triangular Pyramid: F × V = 16

The question asks for the incorrect match. The triangular pyramid's calculated product (16) does not match the expected value (18). Therefore, the incorrect match is:

**Final Answer: Triangular Pyramid (Option 4)**