A polyhedron has 6 faces and 8 vertices. How many edges does it have?

Options

A. 14
B. 15
C. 10
D. 12

Answer

To find the number of edges in a polyhedron with 6 faces and 8 vertices, we can use Euler's formula for polyhedra, which states:

\[ F + V = E + 2 \]

Where:
- \( F \) is the number of faces,
- \( V \) is the number of vertices,
- \( E \) is the number of edges.

### Step-by-step Solution:

1. **Identify the given values**:
- Number of faces \( F = 6 \)
- Number of vertices \( V = 8 \)

2. **Substitute the values into Euler's formula**:
\[ F + V = E + 2 \]
Substituting the known values:
\[ 6 + 8 = E + 2 \]

3. **Calculate the left side**:
\[ 14 = E + 2 \]

4. **Isolate \( E \)**:
To find \( E \), subtract 2 from both sides:
\[ 14 - 2 = E \]
\[ E = 12 \]

5. **Conclusion**:
The number of edges \( E \) is \( 12 \).

### Final Answer:
The polyhedron has **12 edges**.

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