How many diagonals does each of the following have?

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.

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