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Question

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

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Solution


An n-sided convex polygon has n(n-3)2 diagonals.
(i) A quadrilateral has 4(4-3)2 =2 diagonals.
There are 2 diagonals in the convex quadrilateral.

(ii) A regular hexagon has 6(6-3)2=9 diagonals.
There are 9 diagonals in a regular hexagon.

(iii) A triangle does not have any diagonal in it.

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