The diagonal of polygon of \( m \) sides is
A polygon with \(m\) vertices has \(\binom{m}{2}\) line segments joining pairs of vertices. Of these, \(m\) are sides.
Diagonals = \(\binom{m}{2} - m = \frac{m(m-1)}{2} - m = \frac{m(m-3)}{2}\)
Check: a hexagon has \(\frac{6 \times 3}{2} = 9\) diagonals.
Answer: (C) \(\frac{1}{2}m(m-3)\)
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