How many diagonals does a hexagon have?

Get ready for your General Education Test with our structured study tools, featuring flashcards and multiple-choice questions. Access detailed explanations for each question to boost your confidence and ensure a successful exam experience!

Multiple Choice

How many diagonals does a hexagon have?

Explanation:
To count diagonals, think of connecting pairs of vertices that aren’t already connected by a side. A hexagon has 6 vertices. From any one vertex, you can draw diagonals to 3 nonadjacent vertices (you can’t connect to itself or to its two neighbors). That suggests 6 × 3 connections, but each diagonal is counted twice (once from each end), so you divide by 2: 6 × 3 / 2 = 9. Another quick check is to count all pairs of vertices, which is C(6,2) = 15. Subtract the 6 sides, and you’re left with 9 diagonals. So, a hexagon has 9 diagonals.

To count diagonals, think of connecting pairs of vertices that aren’t already connected by a side. A hexagon has 6 vertices. From any one vertex, you can draw diagonals to 3 nonadjacent vertices (you can’t connect to itself or to its two neighbors). That suggests 6 × 3 connections, but each diagonal is counted twice (once from each end), so you divide by 2: 6 × 3 / 2 = 9.

Another quick check is to count all pairs of vertices, which is C(6,2) = 15. Subtract the 6 sides, and you’re left with 9 diagonals.

So, a hexagon has 9 diagonals.

More practice questions