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Find the number of diagonals of

(i) a hexagon

(ii) a polygon of 16 sides

1 Answer

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Best answer

(i) a hexagon

As we know that a hexagon has 6 angular points. By joining those any two angular points we get a line which is either a side or a diagonal.

Therefore number of lines formed = 6C2

On using the formula,

nCr = n!/r!(n – r)!

6C2 = 6!/2!(6 - 2)!

= 6! / (2! 4!)

= [6 × 5 × 4!] / (2! 4!)

= [6 × 5] / (2 × 1)

= 3 × 5

= 15

As we know that number of sides of hexagon is 6

Therefore, number of diagonals = 15 – 6 = 9

Total no. of diagonals formed is 9.

(ii) a polygon of 16 sides

As we know that a polygon of 16 sides has 16 angular points. By joining those any two angular points we get a line which is either a side or a diagonal.

Therefore number of lines formed = 16C2

On using the formula,

nCr = n!/r!(n – r)!

16C2 = 16!/2!(16 - 2)!

= 16! / (2! 14!)

= [16 × 15 × 14!] / (2! 14!)

= [16 × 15] / (2 × 1)

= 8 × 15

= 120

As we know that number of sides of a polygon is 16

Therefore, number of diagonals = 120 – 16 = 104

Total no. of diagonals formed is 104.

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