InterviewSolution
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InterviewSolution
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Find the number of diagonals of(i) a hexagon(ii) a polygon of 16 sides |
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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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