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Earn +20 ptsQ: What geometric that has 3 sides. But how many diagonals does it have?
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How many diagonals does a polygon with 3 sides have?
That polygon is called a "triangle". It has no diagonals.
How many diagonals does a polygon with 100 sides have?
There are: 0.5*(1002-(3*100)) = 4850 diagonals
How many diagonals are there in a polygon of n sides?
n(n-3)/2
How many diagonals does a 20-sides polygon have?
A polygon with n sides had n*(n-3)/2 diagonals. So a 20 sided polygon would have 20*17/3 = 170
How many sides a polygon has with 10 diagonals?
Such a polygon does not exist. A polygon with n sides has 0.5*n*(n-3) diagonals If there are 10 diagonals then 0.5*n*(n-3) = 10 which requires n2 - 3n - 20 = 0 which has no integer roots.
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