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Can a polygon have exactly 10 diagonals?

Updated: 8/16/2019
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13y ago

Best Answer

No not normally.

The formula of the number of diagonals is (n/2)(n - 3).

(n/2)(n - 3) = 10

n(n - 3) = 20

n2 - 3n - 20 = 0 we cannot factor it as (n - r1)(n - r2), where r1 and r2 are natural numbers, so there is any polygon with 10 diagonals.

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13y ago
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9y ago

A polygon with n vertices has n*(n-3)/2 diagonals.A hexagon (n = 6) has 6*3/2 = 9 diagonals while

a heptagon (n= 7) has 7*4/2 = 14 diagonals.

If a polygon were to have exactly 10 diagonals it would have to have between 6 and 7 sides. This is clearly impossible, and so a polygon cannot have exactly 10 sides.


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9y ago

No because there would be a gap in its sides

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Q: Can a polygon have exactly 10 diagonals?
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Under normal scenarios, a polygon cannot have exactly 10 diagonals


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