The number of diagonals in a 27 - sided polygon is

Options

A. 325
B. 320
C. 322
D. 324

Answer

To find the number of diagonals in a 27-sided polygon, we can use the formula for calculating the number of diagonals in a polygon, which is:

\[ \text{Number of Diagonals} = \frac{n(n-3)}{2} \]

where \( n \) is the number of sides of the polygon.

### Step-by-Step Solution:

1. **Identify the number of sides (n)**:
In this case, the polygon has 27 sides, so \( n = 27 \).

2. **Substitute n into the formula**:
We will substitute \( n \) into the formula:
\[ \text{Number of Diagonals} = \frac{27(27-3)}{2} \]

3. **Calculate \( n - 3 \)**:
First, calculate \( 27 - 3 \):
\[ 27 - 3 = 24 \]

4. **Multiply \( n \) by \( n - 3 \)**:
Now, multiply \( 27 \) by \( 24 \):
\[ 27 \times 24 = 648 \]

5. **Divide by 2**:
Finally, divide \( 648 \) by \( 2 \):
\[ \frac{648}{2} = 324 \]

### Conclusion:
The number of diagonals in a 27-sided polygon is **324**.