By using the polygon diagonal formula or the quadratic equation formula in which in both formulae they work out that the polygon in question has 21 sides.
It is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
number of diagonals = n(n-3)/2 n - number of sides of the polygon
1/2*(n2-3n) = 665 diagonals where n means number of sides
Using the formula (x)(x-3)/2 = Diagonals ; simply replace the diagonals with the number of diagonals you're given. Then, you'll havev (x)(x-3)/2 = Diagonals. Simplify it, and you'll be given x(power of 2) - 3X = (2)(Diagonals). Subtract the amount of diagonals from both sides, and you'll have x(power of 2) - 3X - 2Diagonals = 0. From there, use the quadratic formula to find the number of sides the polygon has.
The number of diagonals in a polygon with n sides is n*(n-3)/2 This is double the number of sides so n*(n-3)/2 = 2*n That is n*(n-3) = 4n Dividing both sides by n gives (n-3) = 4 So that n = 7. A heptagon has 7*4/2 = 14 diagonals.
A 7 sided polygon has 14 diagonals
The five sided Polygon has 5 diagonals
The rule is: 0.5*(N2-3N) = number of diagonals
Number of diagonals = 1/2*(n2-3n) where n = the number of sides of the polygon.
38 diagonals
It has 20 diagonals
It is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
The formula is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
A polygon with 14 diagonals will have 7 sides
The equation is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
11
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