Write the number of diagonals of an n-sided polygon.

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Solution

Polygon has n sides and diagonals are kinds made by joining two opposite points = Number of total lines in polygon - Number of sides in the polygon.

Number of diagonals $=^{n} C_{2} - n$

$= \frac{n (n - 1)}{2} - n = n [\frac{n - 1}{2} - 1] = n [\frac{n - 1 - 2}{2}]$

Number of diagonals $= \frac{n (n - 3)}{2}$

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Write the number of diagonals of an n-sided polygon.

Polygon has n sides and diagonals are kinds made by joining two opposite points = Number of total lines in polygon - Number of sides in the polygon. Number of diagonals =nC2−n =n(n−1)2−n=n[n−12−1]=n[n−1−22] Number of diagonals =n(n−3)2