How many diagonals are there in an n- sided polygen ` (n gt 3 ) ? `

Options

A. `(n(n-1))/(2)`
B. `(n(n-3))/(2)`
C. `(n(n+1))/(2)`
D. none of these

Answer

B

Explanation

A polygon of n sides has n vertices. By joining any two vertices of a polygon, we obtain either a side or a diagonal of the polygon. Number of line segments obtained by joining the vertices of a n sided polygon taken two at a time
= Number of ways of selecting 2 out of `n=""^(n)C_(2)=(n(n-1))/(2)`
Out of these lines, n lines are the sides of the polygon.
`:.` Number of diagonals of the polygon `=(n(n-1))/(2)-n`.
`=(n(n-3))/(2)`