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Question
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12
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Solution
Two points are needed to draw a segment.
A polygon of n sides has n vertices.
So, in a polygon of n sides, there will be
nC2 segments, which include its sides and diagonals both.
Since the polygon has n sides, the number of its diagonals is nC2 – n
Here, n = 12
∴ The number of diagonals = 12C2 – 12
= `(12!)/((12 - 2)!2!) - 12`
= `(12 xx 11)/2 - 12`
= 66 – 12
= 54
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