Question 549565: what is the formula for finding the number of diagonals in a shape e.g. triangle has 0 diagonals, quadrilateral has 2 diagonals, pentagon has 5 diagonals, hexagon has 9 diagonals, and so on.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what is the formula for finding the number of diagonals in a shape e.g. triangle has 0 diagonals, quadrilateral has 2 diagonals, pentagon has 5 diagonals, hexagon has 9 diagonals, and so on.
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An n-gon has n vertices.
Each pair of vertices determins a line: nC2 = [n(n-1)]/2] lines
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n of those lines are sides of the n-gon
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So, # of diagonals = nC2 - n
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triangle: # = 3C2-n = 3-3 = 0
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quadrilater: # = 4C2 - 4 = 6-4 = 2
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pentagon: # = 5C2 - 5 = 10-5 = 5
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etc.
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Cheers,
Stan H.
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