Loser66
  • Loser66
I don't understand. Please, help How many diagonals are there in a polygon with 9 sides? The answer is 36
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
With 9 nodes, we pick 2 nodes to form a diagonal, hence there is 9C2 ways to get the diagonals that is 36 ways
jim_thompson5910
  • jim_thompson5910
https://www.mathsisfun.com/geometry/polygons-diagonals.html
Loser66
  • Loser66
However, with the formula \(\dfrac{n(n-3)}{2}\) we get \(dfrac{9(9-3)}{2}=27\) :(

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jim_thompson5910
  • jim_thompson5910
There are n vertices. You can choose n-3 other vertices to make a segment. You cannot choose the two neighboring vertices or the original vertex itself. That's why the "n-3" is there
jim_thompson5910
  • jim_thompson5910
the /2 portion is to correct for double counting
Loser66
  • Loser66
But the 2 answers didn't match. The first one is 36, the second one is 27 , how?
jim_thompson5910
  • jim_thompson5910
36 is incorrect. It must be a typo
jim_thompson5910
  • jim_thompson5910
If it asked "how many distinct line segments can be formed with 9 points?", then the answer would be 36
Loser66
  • Loser66
question 3 http://www.testpreppractice.net/practice-tests/problem-solving-sm/pssm1.html?testname=GRE
jim_thompson5910
  • jim_thompson5910
maybe instead of diagonals, they just meant how many segments were possible
Loser66
  • Loser66
They confuse me a lot. I interpreted it as above, we pick 2 vertices to form a diagonal, hence 9C2 is what they did. But the formula on your site tells me other thing. That's why I make question here. One more thing, 9C2 is a valid logic, right?
jim_thompson5910
  • jim_thompson5910
or maybe they redefined "diagonal", but that doesn't make much sense really
Loser66
  • Loser66
Ok, let me try on smaller number of sides of a polygon. Thanks for clarifying it.
Loser66
  • Loser66
Yes, I think your site is better, just look at a rectangular. Obviously it has 2 diagonals, but if 4C2 = 6 which is total segments on a rectangular, hhehehe.!!!

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