SOLUTION: How many diagonals does a 101-sided convex polygon have than a 100-sided convex polygon?

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Question 420051: How many diagonals does a 101-sided convex polygon have than a 100-sided convex polygon?
Answer by MathLover1(6618) About Me  (Show Source):
You can put this solution on YOUR website!

The number of diagonals in a polygond+=+n%28n-3%29%2F2, where n is the number of polygon sides.

if n=101

d+=+n%28n-3%29%2F2
d+=+101%28101-3%29%2F2
d+=+101%2898%29%2F2
d+=+4949


if n=100

d+=+n%28n-3%29%2F2
d+=+100%28100-3%29%2F2
d+=+100%2897%29%2F2
d+=+4850
4949-4850=99

so, 101-sided convex polygon have 99 more diagonals than a 100-sided convex polygon.