To determine the number of diagonals in a hexagon, follow these steps:
1. Understand the formula: The formula to calculate the number of diagonals in a polygon with [tex]\( n \)[/tex] sides is [tex]\( \frac{n(n-3)}{2} \)[/tex]. This formula arises because each vertex connects to [tex]\( n-3 \)[/tex] other vertices (excluding itself and its two adjacent vertices), and the total number of such connections is divided by 2 to avoid double-counting.
2. Identify the number of sides: For a hexagon, the number of sides [tex]\( n \)[/tex] is 6.
3. Substitute [tex]\( n \)[/tex] into the formula: Using the number of sides of a hexagon in the formula [tex]\( \frac{n(n-3)}{2} \)[/tex]:
[tex]\[
\frac{6(6-3)}{2}
\][/tex]
4. Simplify the expression inside the parentheses:
[tex]\[
6 - 3 = 3
\][/tex]
5. Multiply the values:
[tex]\[
6 \times 3 = 18
\][/tex]
6. Divide by 2:
[tex]\[
\frac{18}{2} = 9
\][/tex]
Thus, there are 9 diagonals in a hexagon.
