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.
Download the pdf of Diagonal of a Polygon Formula
