Geometry

Geometry Level 1

If a polygon has 27 27 diagonals, then the number of sides of the polygon is

12 10 11 9

Ankit Vijay by Ankit Vijay , 22, India

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4 solutions

Krishna Garg
Jun 21, 2014

With the formula for polygon( taking examples of any four sided/five sided figured)we know it is n(n-3)/2,that is how we reach to 9 sided polygon for 27 diagonals. K.K.GARG,India

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You post so many questions Ankit!!!!!

Anuj Shikarkhane - 6 years, 11 months ago

n= number of sides d=number of diagonals ::::::::::::::::: formula: d=n(n-3)/2 ; 27= n^2-3n/2 ; n^2-3n-54=0 ; throw out the negative in (n+6) (n-9) : n=9 - sides ( its a nonagon)

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Manish Mayank
Jun 20, 2014

For any polygon of side "n" No. of diagonals = n ( n − 3 ) 2 \frac{n(n-3)}{2}

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For n-sided polygon no of diagonals is nC2 - n.

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