Find the number of diagonals in an n-sided polygon.

Question:

Find the number of diagonals in an n-sided polygon.

 

Solution:

n-sided polygon has n numbers of vertices. Diagonals are formed by joining

the opposite vertices from one vertex, except the two adjacent vertices. So, from one vertex $(n-3)$ diagonals can be drawn. Similarly, for $n$ numbers of vertices, $n(n-3)$ diagonals can be drawn. But, the diagonal joins 2 points at a time, here two

vertices. Therefore, the actual number of diagonals is $=\frac{n(n-1)}{2}$.

 

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