Solution
Polygon Diagonals
Show the problem again
How many diagonals does a convex 12-sided polygon have?
Worked solution
The answer is 54. Each vertex connects by diagonal to all vertices except itself and its two neighbors: 9 diagonals per vertex. Multiplying by 12 vertices counts each diagonal twice, so the total is 12 · 9 / 2 = 54. Generally an n-gon has n(n − 3)/2 diagonals.
Source: Standard polygon-diagonal counting exercise from introductory combinatorics texts. Statement written for AxiomIQ.