Suppose the polygon has n sides. Then n*(n-3)/2 = 54
or n*(n-3) = 108
and so, by inspection, n = 12
or you can multiply out the brackets and solve the quadratic equation in n.
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how many diagonals are there iin a polygon of 11 sides
For a polygon with n sides, there would be n*(n-3)/2
That polygon is called a "triangle". It has no diagonals.
It depends if the polygon is convex or concave but if it is a regular polygon it would have 560
A polygon with 14 diagonals will have 7 sides