Which of the following options represents the incorrect match of the given geometrical shapes and their number of edges.

Options

A. Triangular Prism - 9
B. Rectangular Pyramid - 8
C. Pentagonal Prism - 15
D. Octahedron - 24

Answer

To solve the problem of identifying the incorrect match of geometrical shapes and their number of edges, we will analyze each shape one by one.

### Step-by-Step Solution:

1. **Identify the Shapes**: The shapes we need to analyze are:
- Triangular Prism
- Rectangular Pyramid
- Pentagonal Prism
- Octahedron

2. **Count the Edges of Each Shape**:

**a. Triangular Prism**:
- A triangular prism has two triangular bases and three rectangular faces.
- The edges can be counted as follows:
- Base triangle edges: 3 edges
- Top triangle edges: 3 edges
- Vertical edges connecting the two triangles: 3 edges
- Total edges = 3 (base) + 3 (top) + 3 (vertical) = 9 edges.

**b. Rectangular Pyramid**:
- A rectangular pyramid has a rectangular base and four triangular faces.
- The edges can be counted as follows:
- Base rectangle edges: 4 edges
- Vertical edges connecting the apex to each corner of the base: 4 edges
- Total edges = 4 (base) + 4 (vertical) = 8 edges.

**c. Pentagonal Prism**:
- A pentagonal prism has two pentagonal bases and five rectangular faces.
- The edges can be counted as follows:
- Base pentagon edges: 5 edges
- Top pentagon edges: 5 edges
- Vertical edges connecting the two pentagons: 5 edges
- Total edges = 5 (base) + 5 (top) + 5 (vertical) = 15 edges.

**d. Octahedron**:
- An octahedron has 8 triangular faces.
- The edges can be counted as follows:
- The octahedron has 12 edges in total.
- Total edges = 12 edges.

3. **Match the Counts with Given Options**:
- Triangular Prism: 9 edges (Correct)
- Rectangular Pyramid: 8 edges (Correct)
- Pentagonal Prism: 15 edges (Correct)
- Octahedron: 12 edges (Incorrect if the question states it has 8 edges)

4. **Conclusion**: The incorrect match is the octahedron, which should have 12 edges, not 8.

### Final Answer:
The option that represents the incorrect match is the octahedron.