Defining a diagonal as any two vertices that are not connected by an edge (non-adjacent) of the polygon, you can determine the amount of diagonals using the following formula
s = sides in polygon
(s*(s-3))/2
So,
(3*(3-3))/2 = 0
(4*(4-3))/2 = 2
(5*(5-3))/2 = 5
(6*(6-3))/2 = 9
(7*(7-3))/2 = 14
(8*(8-3))/2 = 20
(9*(9-3))/2 = 27
(10*(10-3))/2 = 35
(11*(11-3))/2 = 44
So, the polygon would have to have somewhere between 10 and 11 sides. Since a polygon can not have fractional amount of sides, no polygon exists that has 42 diagonals.
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The formula is: 0.5*(n2-3n) where n is the number of sides of the polygon
0.5*(n2-3n) where n is equal to the number of sides of the polygon
You can use the formula D=S-2 where D is the number of possible diagonals and S is the number of sides the polygon has.
There are 44 diagonals in an 11-sided polygon. heres how to find the amount of diagonals: S=amount of sides 1/2 S(S-3)