Question 420051

The number of diagonals in a polygon{{{d = n(n-3)/2}}}, where {{{n}}} is the number of polygon {{{sides}}}.


if {{{n=101}}}


{{{d = n(n-3)/2}}}

{{{d = 101(101-3)/2}}}

{{{d = 101(98)/2}}}

{{{d = 4949}}}



if {{{n=100}}}


{{{d = n(n-3)/2}}}

{{{d = 100(100-3)/2}}}

{{{d = 100(97)/2}}}

{{{d = 4850}}}

{{{4949-4850=99}}}


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