What is the name of the polygon with 27 diagonals?

formula for diagonal of a polygon:

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

Given: 27 diagonals

Sol'n:

27 = (n^2 - 3n) / 2

2 ( 27 = (n^2 - 3n) / 2 ) 2

54 = n^2 - 3n      or    n^2 - 3n = 54

n^2 - 3n - 54 = 0

( n - 9 ) ( n + 6 ) = 0

n - 9 = 0      and      n + 6 = 0

n = 9                        n = -6

There's no negative side so the valid side is 9

Nonagon is the final answer.