If \(n\) is the number of sides of a polygon, then the number of its diagonals is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{n(n-3)}{2}\)
A diagonal joins two vertices that are not neighbours.
From one vertex, diagonals go to every vertex except itself and its two neighbours: \(n-3\) diagonals
For all \(n\) vertices this gives \(n(n-3)\), but each diagonal has two ends and is counted twice
Number of diagonals \(\displaystyle=\frac{n(n-3)}{2}\); for example, a square (\(n=4\)) has \(\frac{4\times1}{2}=2\)