A hexagon is a 6-sided polygon with 6 vertices and 6 sides.
A diagonal is a line that connects two non-adjacent vertices. The sides of the hexagon are not diagonals.
For any polygon with n sides, the number of diagonals is:
Number of Diagonals =2n(n−3)
For a hexagon, n=6:
Number of Diagonals =26(6−3)
=26(3)
=218
=9
From any vertex, lines can be drawn to other vertices:
Total vertices =6
Excluding the vertex itself =6−1=5
Excluding the 2 adjacent vertices (which form sides, not diagonals) =5−2=3 diagonals per vertex
Total lines from all 6 vertices:
6×3=18
Each diagonal is counted twice (once from each endpoint):
Actual number of diagonals =218=9
Therefore, the number of diagonals in a hexagon is 9.