Diagonal of a Polygon Formula

Before understanding the diagonal of a polygon formula, let's review what a polygon is and what a diagonal is. A closed shape made up of three or more line segments is called a polygon. A polygon's diagonal is a line segment formed by connecting any two non-adjacent vertices.

Define Diagonal of a Polygon Formula:

Several diagonals in a polygon are calculated using the diagonal of a polygon formula. It states that the number of diagonals in a polygon is equal to n(n-3)/2. You can get all Maths formulas on one-page visit the Maths Formulas section of HT.

'n' denotes the number of sides that a polygon has.

Example: Using the diagonal of a polygon formula, determine the number of diagonals in a decagon.

Sol: 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

Solved example of Diagonal of a Polygon Formula

Example: How many sides does a polygon have if it has 90 diagonals?

Sol: Let us suppose 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

n²−3n−180 = 0

(n−15)(n+12) = 0

n = 15;n = −12

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

Diagonal of a Polygon Formula