Question

How many diagonals does each of the following have?
(i) A convex quadrilateral
(ii) A regular hexagon
(iii) A triangle.

Answer 1

(i) A convex qudrilateral
Here n=4
$\therefore$ Nimber of diagonals =$\frac{n(n-3)}{2}$ diagonal
$=\frac{4(4-3)}{2}=\frac{4\times 1}{2}=2$ diagonal
(ii) A regular hexagon
Here n=6
$\therefore$ Number of diagonals =$\frac{n(n-3)}{2}$
$=\frac{6(6-3)}{2}=\frac{6\times 3}{2}=9$ diagonal
(iii) A triangle
Here n=3
$\therefore$ Number of diagonals = $\frac{n(n-3)}{2}$
$=\frac{3(3-3)}{2}=0$ diagonal. Ans.