How many diagonals are in an irregular polygon?

Answer 1

The formula which tells you the number of diagonals possible in a regular polygon is:

the number of points (or sides), which we will call 'n', multiply by (n-3). Then divide the answer by 2.

This will give you the number of diagonals.

Formula: n X (n-3)/2

Examples

A square has four sides.

4 X (4-3) = 2

Divide 2 by 2 = 2

So a square, a 4-sided polygon, has two diagonals.

A pentagon has five sides

5 X (5-3) = 10

Divide 10 by 2 = 5

So a 5-sided polygon has 5 diagonals

Using the same formula we can calculate the number of diagonals of any regular polygon.

e.g. 13-sides

13 X (13-3) = 130

Divide 130 by 2 = 65

So a 13-sided polygon has 65 diagonals!

If a polygon is irregular, meaning that its sides are of different lengths, and if all the points of the polygon are pointing outwards, the same formula holds true.

But if the polygon is so irregular that some of its angles point inwards, there is no way of computing the number of diagonals because, in some irregular polygons, some potential diagonals may be impossible to reach from one point to the other without going outside the boundary of the polygon.