Question

Question 92:

The number of diagonals of an n-sided figure is $\frac{1}{2}(n^2-3n)$. Use the formula to find the number of diagonals for a 6-sided figure(hexagon).

Answer 1

Given, a polygon has n sides, then number of diagonals is $\frac{1}{2}(n^2-3n)$.
In hexagon, there are 6 sides.
Therefore for calculating number of diagonals in hexagon, put n=6 in the above formula.
$\therefore$ Number of diagonals= $\frac{1}{2}[n^2-3n]=\frac{1}{2}(6^2-3\times 6)=\frac{1}{2}(6\times 6-3\times 6)=\frac{1}{2}(36-18)=\frac{1}{2}\left(18\right)=9$
Hence, a hexagon has 9 diagonals.