Find the number of diagonals of

(i) a hexagon

(ii) a polygon of 16 sides

Asked by Aaryan | 1 year ago |  45

Solution :-

(i) a hexagon

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.

So number of lines formed = 6C2

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

6C2 =$$\dfrac{6!}{2!(6-2)!}$$

=$$\dfrac{ 6×5 }{ (2×1)}$$

= 3×5

= 15

We know number of sides of hexagon is 6

So, number of diagonals = 15 – 6 = 9

The total no. of diagonals formed is 9.

(ii) a polygon of 16 sides

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.

So number of lines formed = 16C2

By using the formula,

nCr =$$\dfrac{ n!}{r!(n – r)!}$$

16C2 = $$\dfrac{ 16!}{2!(16-2)!}$$

= $$\dfrac{ 16×15 }{ (2×1)}$$

= 8×15

= 120

We know number of sides of a polygon is 16

So, number of diagonals = 120 – 16 = 104

The total no. of diagonals formed is 104.

Answered by Sakshi | 1 year ago

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