Question

if the number of diagonals of a polygon is given give the formula to find its sides​

Answer 1

By using the formula for the number of diagonals of a polygon with n sides, you can determine how many sides a polygon has if you know the number of diagonals it has. For example, if a polygon has 54 diagonals, find how many sides it has.

Remember, the formula is:

diag = n*(n - 3)/2

Plugging in the known information, we know that diag = 54. So,

54 = n*(n - 3)/2

Then, solve for n using algebra. First multiply both sides by 2.

54*2 = 108 = n*(n - 3)

108 = n2 - 3n

Notice there is a squared term. This is a quadratic equation, so we can solve it either by factoring or using the quadratic formula. Here, we'll use factoring.

0 = n2 - 3n - 108

0 = (n - 12)(n + 9)

So, n = 12 or -9. But, since a polygon cannot have a negative number of sides, we know that this polygon must have 12 sides.

Answer 2

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The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).

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