(i) A convex quadrilateral
Convex quadrilateral has two diagonals.
(ii) A regular hexagon
An n-sided convex polygon has \(\frac{n(n-3)}{2}\) diagonals.
∴ Applying the above relation for hexagon:
Number of diagonals = \(\frac{6(6-3)}{2}\) = \(\frac{18}{2}\) = 9
Regular Hexagon has 9 diagonals.
(iii) A triangle
An n-sided convex polygon has \(\frac{n(n-3)}{2}\) diagonals.
∴ Applying the above relation for triangle:
Number of diagonals = \(\frac{3(3-3)}{2}\) = 0
Therefore a triangle has no diagonal
