Find the number of diagonals formed in hexagon.

Options

A. 12
B. 10
C. 6
D. 9

Answer

To find the number of diagonals in a hexagon, we can use the formula for the number of diagonals in a polygon, which is given by:

\[ D = \frac{n(n - 3)}{2} \]

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

### Step-by-Step Solution:

1. **Identify the number of sides (n)**:
- A hexagon has 6 sides. Therefore, \( n = 6 \).

2. **Substitute n into the formula**:
- We substitute \( n \) into the diagonal formula:
\[ D = \frac{6(6 - 3)}{2} \]

3. **Simplify the expression**:
- Calculate \( 6 - 3 \):
\[ 6 - 3 = 3 \]
- Now substitute back into the formula:
\[ D = \frac{6 \times 3}{2} \]

4. **Calculate the product**:
- Multiply \( 6 \) and \( 3 \):
\[ 6 \times 3 = 18 \]

5. **Divide by 2**:
- Now divide \( 18 \) by \( 2 \):
\[ D = \frac{18}{2} = 9 \]

6. **Conclusion**:
- Therefore, the number of diagonals in a hexagon is \( 9 \).

### Final Answer:
The number of diagonals formed in a hexagon is **9**.