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

1.	Find the number of diagonals in an n-sided polygon.
Answer» 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 \(=\frac{n(n-1)}{2}.\)

Answer»

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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