# Diagonal Of Polygon Formula

## Diagonal Of A Polygon Formula

A polygon is simply a simple figure surrounded by straight lines. Poly means many in Greek, and gon means angle. The most basic polygon is a triangle with three sides and angles that add up to 180 degrees. Polygons with many sides can either be regular (with equal lengths and interior angles) or irregular. The interior angles of a polygon can further categorise it as concave or convex. The polygon is convex if the interior angles are less than 180 degrees; otherwise, it is concave. It is worth noting that the sides of a polygon are always straight lines.

The Diagonal Of Polygon Formula is the line segment that connects two non-adjacent vertices. Concave polygons have at least one diagonal outside the polygon, an interesting fact about a polygon’s diagonals.

Any line segment joining two non-adjacent vertices is considered the Diagonal Of Polygon Formula. Depending on the type of polygon and the number of sides, different diagonals have different properties. Before learning the Diagonal Of Polygon Formula, students must review what a polygon and a diagonal are.

A polygon is a closed shape of three or more line segments. The diagonal of a polygon is a line segment created by connecting any two non-adjacent vertices. Here are some examples of problems that have been solved and the Diagonal Of Polygon Formula. A basic polygon with a few sides allows one to count all possible diagonals quickly. When polygons become more intricate, counting them can become difficult.

What Is the Diagonal of a Polygon Formula?

The number of diagonals can be determined using the Diagonal Of Polygon Formula. It states

The number of Diagonal Of Polygon Formula = n(n−3)/2

Here

‘n’ is the number of sides the polygon has.

### Examples Using Diagonal Of A Polygon Formula

• Example 1: Find the number of diagonals of a decagon using the Diagonal Of Polygon Formula.

Solution:

The number of sides of a decagon is, n=10

The number of diagonals of a decagon is calculated using:

n(n−3)/2=10(10−3)/2

=10(7)/2=70/2=35

Answer: The number of diagonals of a decagon= 35

• Example 2: If a polygon has 90 diagonals, how many sides does it have?

Solution:

Let us assume that the number of sides of the given polygon is n.

The number of diagonals = 90.

Using the Diagonal Of Polygon Formula,

n(n−3)/2=90

n(n−3)=180

n2−3n−180=0

(n−15)(n+12)=0

n=15;n=−12

Since n cannot be negative, the value of n is 15.

Answer: Sides of the given polygon = 15.