Q&A #3829

Diagonals of polygons

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From: Jim and Carolyn (for Teacher2Teacher Service)
Date: May 01, 2000 at 16:37:11
Subject: Re: Diagonals of polygons

The formula to find the number of diagonals d in terms of the number of
sides n is:   d = (n(n - 3))/2.  For example, in a pentagon the number of
sides n is 5, so d = 5(5 - 3)/2 = 5.
   To understand the formula pick a vertex on a pentagon.  Notice from that
vertex you can draw exactly 2 diagonals, thus the  n - 3 in the formula.
Repeat this at each vertex which would make it appear to be 10 diagonals.
However, each diagonal would have been drawn twice. (So divide by 2.)

 -Jim and Carolyn, for the Teacher2Teacher service

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