# Help

can anyone help me? one of my friends asked me that. how many diagonals are there in a 200 sided polygon.... as assumption she said tht triagles had no diagonals and rectangles had 2 diagonals...

3 years, 8 months ago

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200C2-200=19700. Total 19700 diagonals

- 3 years, 8 months ago

but what is the reason?? what is the relattion with the assumption

- 3 years, 8 months ago

See, If you know about the permutations and combinations. If n points are given to you, you can draw nC2 lines from them, given none of them are collinear. In a polygon, at most 2 points can be collinear. You need two pints 2 draw a line. So, indirectly we are finding the number of ways of selecting 2 points out of 200 = 200C2. Now these lines will also contain the sides of the polygon, So, to ignore them, we need to subtract the number of sides, which is equal to 200. Therefore, total number of diagonals = 200C2-200 = 19700

- 3 years, 8 months ago

i asked her and she said its just n(n-3)/2....

- 3 years, 8 months ago

Yess...(nc2-n) on solving gives us (n(n-3)/2)

- 3 years, 8 months ago

nC2- n where n is the number of sides in the polygon, would give you the number of diagonals. So 19700

- 3 years, 8 months ago

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