Diagonal of a Polygon Formula
Before going to learn the diagonal of a polygon formula, let us recall what is a polygon and what is a diagonal. A polygon is a closed shape made with 3 or more line segments, A diagonal of a polygon is a line segment that is obtained by joining any two nonadjacent vertices. Let us learn the diagonal of a polygon formula along with a few solved examples.
What Is the Diagonal of a Polygon Formula?
The diagonal of a polygon formula is used to calculate the number of diagonals of a polygon. It says
The number of diagonals of a polygon = n(n−3)/2
Here
 'n' is the number of sides polygon has.
Let us see the applications of the diagonal of a polygon formula in the following section.

Example 1: Find the number of diagonals of a decagon using the diagonal of a 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 9090 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 a polygon formula,
n(n−3)/2=90
n(n−3)=180
n^{2}−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.