Question

Number of sides of polygon with number of diagonals

Answer 1

The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).

Answer 2

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• According to the formula, number of diagonals = n (n-3)/ 2. So, 11-sided polygon will contain 11(11-3)/2 = 44 diagonals.

→Number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides.

→To find the total number of diagonals in a polygon, multiply the number of diagonals per vertex (n - 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice).