# Formula for number of diagonals of a polygon

Learn and know the formula to find the number of diagonals of a polygon. We know that each and every polygon will be having some diagonals. But the total number of diagonals that a polygon has, we can’t say the exact number by looking at the polygon. We can also draw the diagonals and count the number of diagonals that a polygon contains. But it takes lot of time to draw and count number of diagonals. To know the exact number of diagonals for a polygon, we need to learn its formula. It makes us to find easily the number of diagonals.

## Formula for finding number of diagonals of a polygon is given below

Let us consider a polygon which contains “n” sides. Now the formula for number of diagonals is given by n (n – 3)/2 where “n” stands for number of sides.

Example:

Let us consider a polygon which has 3 sides i.e. triangle. Now by applying formula we will find out the number of diagonals for a triangle. According to formula, number of diagonals = n (n – 3)/2 = 3 (3 – 3)/2 = 0/2 = 0.

Now we will consider one more polygon which has 8 sides i.e. octagon. Number of diagonals of an octagon = n (n – 3)/2 = 8 (8-3)/2 = 40/2 = 20. Therefore we can say that the polygon octagon has totally 20 diagonals.

Number of diagonals of a polygon which has 5 sides = n (n – 3)/2 = 5 (5-3)/2 = 10/2 = 5

Number of diagonals of a polygon which has 6 sides = n (n – 3)/2 = 6 (6-3)/2 = 18/2 = 9

Number of diagonals of a polygon which has 7 sides = n (n – 3)/2 = 7 (7-3)/2 = 28/2 = 14

Number of diagonals of a polygon which has 9 sides = n (n – 3)/2 = 9 (9-3)/2 = 54/2 = 27

Number of diagonals of a polygon which has 10 sides = n (n – 3)/2 = 10 (10-3)/2 = 70/2 = 35 