## DIAGONAL

A diagonal is a plane line that acts as a connecting path for two corners that are opposite from each other with the help of its vertices. Thus, a polygon’s diagonal is a transmission line that connects two different edges. Based on the number of edges, various polygons might have a varying number of diagonals. A diagonal is called a straight line because it is a line segment connecting non-adjacent vertices.

- If “n” is the set of vertices in a polygon, then the total number of diagonals in a given shape can be calculated using the following formula: [n× (n-3)]/2
- The number of diagonals in a geometric shape with “n” vertices is equal to [n× (n-3)]/2
- Different shapes have differing amounts of diagonals of varying lengths.

Let us now look at the diagonals of some geometric shapes.

- Diagonals of Triangle
- Diagonals of decagon
- Diagonals of octagon
- Diagonals of hexagon
- Diagonals of Parallelogram
- Diagonals of heptagon
- Diagonals of hexagon

Types of polygon | No of vertices | Method of calculating | Resulting number of diagnoal |

Decagon | 10 | [10×(10-3)]/2 | 35 |

Octagon | 8 | [8×(8-3)]/2 | 20 |

Heptagon | 7 | [7×(7-3)]/2 | 14 |

Pentagon | 5 | [5×(5-3)]/2 | 5 |

Hexagon | 6 | [6×(6-3)]/2 | 9 |

Triangle | 3 | [3×(3-3)]/2 | 0 |

### SOLVED EXAMPLES

**Example 1: **suppose there is a polygon and it is having with having total of 20 diagonals, then by the help of formula and doing the evaluation find out the total number of sides does the polygon have

**Solution:**

Let us take the total number of side of the given polygon to be n.

And the given information states that total diagonals = 20.

Applying the diagonal of a polygon formula we get

- N× (n−3)/2 =20
- N× (n−3) =40
- n2−3n−40=0
- (n−8)(n+5)=0
- n=8 or n=−5

Since n can never be a negative value so, the value of n is taken as 8