Counting Sides by Counting DiagonalsDate: 06/04/2002 at 07:41:53 From: Sunita Subject: Sides in a Polygon I wish to have a formula that can tell me how to calculate the number of sides of a polygon if I know the number of diagonals in that polygon. For example, I know that the number of diagonals in a polygon is 44. How many sides does this polygon have? Date: 06/04/2002 at 07:48:45 From: Doctor Ian Subject: Re: Sides in a Polygon Hi Sunita, Suppose you have a polygon with N vertices. From each vertex, you can draw a diagonal to (N-3) other vertices, so the number of directed diagonals is N(N-3). However, when you do this, you end up with diagonals going in both directions, so you want to cut the number in half. So the number of undirected diagonals is N(N-3)/2. Convince yourself that this works for any N. To go from the number of diagonals to the number of vertices, you just go in the other direction: 44 = N(N-3)/2 88 = N(N-3) 11 = N So the polygon has 11 sides. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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