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Polygon Diagonals

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Polygon Diagonals

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). However, this would mean that each diagonal would be drawn twice, (to and from each vertex), so the expression must be divided by 2.

For more discussion, see the Dr. Math archives:

Counting Diagonals
How many diagonals can be drawn for a polygon with n sides?

Diagonals of Polygons
How many diagonals does a polygon with n sides have?

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Middle School Triangles/Polygons
High School Triangles/Polygons
Index of Selected Answers to Common Questions

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