Question

The number of diagonals of an n-sided figure is `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 `1/2(n^2 - 3n)`

In hexagon, there are six sides

Therefore for calculating number of diagonals in hexagon, put n = 6 in the above formula

∴ Number of diagonals = `1/2[n^2 - 3n]`

= `1/2(6^2 - 3 xx 6)`

= `1/2(6 xx 6 - 3 xx 6)`

= `1/2(36 - 18)`

= `1/2(18)`

= 9

Hence, a hexagon has 9 diagonals.