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Question
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
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 = 10
∴ The number of diagonals = 10C2 – 10
= `(10!)/((10 - 2)!2!) - 10`
= `(10 xx 9)/2 - 10`
= 45 – 10
= 35.
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