SOLUTION: what is the maximum number of diagonals can be drawn in a n-sided polygon?

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Question 556823: what is the maximum number of diagonals can be drawn in a n-sided polygon?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
An n-sided polygon has n sides and n vertices.

Every diagonal and every side of the polygon is the line segment 
connecting a combination of two vertices.  

Every combination of 2 vertices uniquely represents either a side
or a diagonal. 

Derivation of the formula:

1. First we get the number of sides and diagonals by getting the
   number of combinations of n vertices taken 2 at a time:

   C(n,2) = n%28n-1%29%2F2 

2. To get the number of diagonals only, we must subtract the number 
   of sides, which is n. 

   n%28n-1%29%2F2 - n

3. We get an LCD of 2 and simplify:

    n%28n-1%29%2F2 - 2n%2F2

    %28n%5E2-n%29%2F2 = 2n%2F2

    %28n%5E2-n-2n%29%2F2

    %28n%5E2-3n%29%2F2

    %28n%28n-3%29%29%2F2

So if d represents the number of diagonals of 
an n-sided polygon, then the formula is

d = n%28n-3%29%2F2

Edwin