9. How many vertices, edges, and faces are there for the polyhedron? * B E H 5. 8. 15 10 12 faces vertices edges

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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### Understanding Polyhedrons: Vertices, Edges, and Faces

In this exercise, you are asked to determine the number of vertices, edges, and faces of the given polyhedron.

#### Diagram Explanation

The given diagram depicts a 3-dimensional geometric figure, known as a polyhedron. Each vertex of the polyhedron is labeled with a letter from A to H. The key components of the polyhedron are:

- **Vertices** (Corners): Points where two or more edges meet.
- **Edges** (Lines): Line segments between vertices.
- **Faces** (Surfaces): Flat surfaces enclosed by edges.

Here, our task is to identify the exact number of each of these components.

#### Multiple Choice Options

The table below the diagram offers a selection of possible answers with respect to the number of vertices, edges, and faces:

| Faces | Vertices | Edges |
|-------|----------|-------|
| 5     | 8        | 5     |
| 6     | 8        | 12    |
| 10    | 15       | 8     |
| 12    | 10       | 6     |

You need to select the correct combination by analyzing the polyhedron described in the diagram.

By closely inspecting the diagram:

1. **Vertices (Corners)**: The polyhedron has 8 vertices labeled as A, B, C, D, E, F, G, and H.
2. **Edges (Lines)**: The polyhedron has 12 edges, including each outer connecting edge and the internal edges connecting vertices.
3. **Faces (Surfaces)**: The polyhedron has 6 faces, as observed from the depiction of its surfaces.

### Conclusion

Based on the diagram analysis, the appropriate selection is: 

- **Vertices**: 8
- **Edges**: 12
- **Faces**: 6

These characteristics correspond to the multiple-choice option:
| 6 | 8 | 12 |
Transcribed Image Text:### Understanding Polyhedrons: Vertices, Edges, and Faces In this exercise, you are asked to determine the number of vertices, edges, and faces of the given polyhedron. #### Diagram Explanation The given diagram depicts a 3-dimensional geometric figure, known as a polyhedron. Each vertex of the polyhedron is labeled with a letter from A to H. The key components of the polyhedron are: - **Vertices** (Corners): Points where two or more edges meet. - **Edges** (Lines): Line segments between vertices. - **Faces** (Surfaces): Flat surfaces enclosed by edges. Here, our task is to identify the exact number of each of these components. #### Multiple Choice Options The table below the diagram offers a selection of possible answers with respect to the number of vertices, edges, and faces: | Faces | Vertices | Edges | |-------|----------|-------| | 5 | 8 | 5 | | 6 | 8 | 12 | | 10 | 15 | 8 | | 12 | 10 | 6 | You need to select the correct combination by analyzing the polyhedron described in the diagram. By closely inspecting the diagram: 1. **Vertices (Corners)**: The polyhedron has 8 vertices labeled as A, B, C, D, E, F, G, and H. 2. **Edges (Lines)**: The polyhedron has 12 edges, including each outer connecting edge and the internal edges connecting vertices. 3. **Faces (Surfaces)**: The polyhedron has 6 faces, as observed from the depiction of its surfaces. ### Conclusion Based on the diagram analysis, the appropriate selection is: - **Vertices**: 8 - **Edges**: 12 - **Faces**: 6 These characteristics correspond to the multiple-choice option: | 6 | 8 | 12 |
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