If a, b and c are respectively the number of faces, edges and vertices of a pentagonal pyramid, then the value of `((a-b+c)/(2))-2` is

Options

A. `-15`
B. 2
C. 1.75
D. `-1`

Answer

To solve the problem, we need to determine the values of \( a \), \( b \), and \( c \) for a pentagonal pyramid, which represent the number of faces, edges, and vertices respectively.

### Step-by-Step Solution:

1. **Identify the number of faces (a)**:
A pentagonal pyramid has a pentagonal base and 5 triangular faces that connect the base to the apex. Therefore, the total number of faces \( a \) is:
\[ a = 1 \text{ (pentagonal base)} + 5 \text{ (triangular faces)} = 6 \]

2. **Identify the number of edges (b)**:
The pentagonal base has 5 edges, and there are 5 edges connecting the apex to each vertex of the base. Therefore, the total number of edges \( b \) is:
\[ b = 5 \text{ (base edges)} + 5 \text{ (edges to apex)} = 10 \]

3. **Identify the number of vertices (c)**:
The pentagonal base has 5 vertices, and there is 1 additional vertex at the apex. Therefore, the total number of vertices \( c \) is:
\[ c = 5 \text{ (base vertices)} + 1 \text{ (apex)} = 6 \]

4. **Substitute the values into the expression**:
We need to calculate the expression \( \frac{(a - b + c)}{2} - 2 \):
\[ a - b + c = 6 - 10 + 6 = 2 \]
Now, substitute this into the expression:
\[ \frac{(2)}{2} - 2 = 1 - 2 = -1 \]

5. **Final answer**:
Therefore, the value of \( \frac{(a - b + c)}{2} - 2 \) is:
\[ \boxed{-1} \]