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Question
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12
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Solution
In an n-sided polygon, there are ‘n’ points and ‘n’ sides.
∴ Through ‘n’ points we can draw nC2 lines including sides.
∴ Number of diagonals in n sided polygon
= nC2 – n ...(n = number of sides)
n = 12, nC2 – n = 12C2 – 12
= `(12 xx 11)/(1 xx 2) - 12`
= 66 – 12
= 54
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