Question:
How many diagonals does each of the following have?
(i) A convex quadrilateral
(ii) A regular hexagon
(iii) A triangle
Solution:
An $\mathrm{n}$-sided convex polygon has $\frac{n(n-3)}{2}$ diagonals.
(i) A quadrilateral has $\frac{4(4-3)}{2}=2$ diagonals.
There are 2 diagonals in the convex quadrilateral.
(ii) A regular hexagon has $\frac{6(6-3)}{2}=9$ diagonals.
There are 9 diagonals in a regular hexagon.
(iii) A triangle does not have any diagonal in it.