# 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 $\frac { n\left( n-3 \right) }{ 2 }$ 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 = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 3\left( 3-3 \right) }{ 2 }$ = $\frac { 0 }{ 2 }$ = 0.

Now we will consider one more polygon which has 8 sides i.e. octagon. Number of diagonals of an octagon = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 8\left( 8-3 \right) }{ 2 }$ = $\frac { 40 }{ 2 }$ = 20. Therefore we can say that the polygon octagon has totally 20 diagonals.

Number of diagonals of a polygon which has 5 sides = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 5\left( 5-3 \right) }{ 2 }$ = $\frac { 10 }{ 2 }$ = 5

Number of diagonals of a polygon which has 6 sides = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 6\left( 6-3 \right) }{ 2 }$ = $\frac { 18 }{ 2 }$ = 9

Number of diagonals of a polygon which has 7 sides = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 7\left( 7-3 \right) }{ 2 }$ = $\frac { 28 }{ 2 }$ = 14

Number of diagonals of a polygon which has 9 sides = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 9\left( 9-3 \right) }{ 2 }$ = $\frac { 54 }{ 2 }$ = 27

Number of diagonals of a polygon which has 10 sides = $\frac { n\left( n-3 \right) }{ 2 }$ = $\frac { 10\left( 10-3 \right) }{ 2 }$ = $\frac { 70 }{ 2 }$ = 35