The polygon has nine sides. It is called a

*.***nonagon**The polygon has nine sides. It is called a **nonagon**.

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.

A nine sided shape has 27 diagonals because:

Formula: N(n-3)/2

9(9-3)/2 = 9*6/2 = 27 diagonals

Formula: N(n-3)/2

9(9-3)/2 = 9*6/2 = 27 diagonals

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