Math Formula for Diagonals
2026-02-28 01:38 Diff

214 Learners

Last updated on August 9, 2025

In geometry, understanding diagonals is crucial for analyzing the properties of polygons. A diagonal is a line segment connecting two non-adjacent vertices of a polygon. In this topic, we will learn the formula to determine the number of diagonals in a polygon based on the number of its sides.

List of Math Formulas for Diagonals in Polygons

The formula to calculate the number of diagonals in a polygon is essential in geometry. Let’s learn the formula to calculate the diagonals in any polygon.

Math Formula for Diagonals in Polygons

A diagonal is a line segment connecting two non-adjacent vertices in a polygon. The formula to calculate the number of diagonals in a polygon with n sides is:

Diagonals = n(n-3)/2

Where n represents the number of sides in the polygon.

Understanding the Diagonals Formula

The formula for the number of diagonals is derived by considering each vertex of the polygon, which can connect to any of the other n-3 vertices (excluding itself and its two adjacent vertices). Thus, the total number of connections (or diagonals) is divided by 2, as each diagonal is counted twice.

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Examples of Calculating Diagonals

Consider a pentagon, which has 5 sides.

Using the diagonal formula:

Diagonals = 5(5-3)/2 = 5

In a hexagon with 6 sides:

Diagonals = 6(6-3)/2 = 9

Importance of the Diagonals Formula

The diagonals formula is used in various geometric problems and proofs. By understanding this formula, students can easily analyze complex polygonal shapes and their properties. It also aids in visualizing the internal structure of polygons.

Tips and Tricks to Memorize the Diagonals Formula

Students often find geometry formulas challenging. To memorize the diagonals formula, remember that you subtract 3 from the number of sides to account for the vertices that cannot form diagonals (itself and two adjacent vertices) and divide by 2 because each diagonal is counted twice.

Common Mistakes and How to Avoid Them While Using the Diagonals Formula

Students often make errors when calculating the number of diagonals. Here are some common mistakes and tips to avoid them.

Problem 1

How many diagonals are there in an octagon?

Okay, lets begin

There are 20 diagonals in an octagon.

Explanation

Using the formula:

Diagonals = 8(8-3)/2 = 20

Well explained 👍

Problem 2

Find the number of diagonals in a decagon.

Okay, lets begin

A decagon has 35 diagonals.

Explanation

Using the formula:

Diagonals = 10(10-3)/2 = 35

Well explained 👍

Problem 3

Calculate the number of diagonals in a heptagon.

Okay, lets begin

There are 14 diagonals in a heptagon.

Explanation

Using the formula:

Diagonals = 7(7-3)/2 = 14

Well explained 👍

FAQs on Diagonals Formula

1.What is the formula for the number of diagonals in a polygon?

The formula to find the number of diagonals in a polygon is:

Diagonals = n(n-3)/2, where n is the number of sides.

2.Can the diagonals formula be applied to any shape?

No, the diagonals formula is specifically for polygons, as it requires a closed shape with sides.

3.What is the significance of the diagonals formula?

The diagonals formula helps in understanding the internal structure and properties of polygons, which is useful in various applications like geometry, design, and architecture.

4.How do you calculate the number of diagonals in a dodecagon?

For a dodecagon (12 sides), the number of diagonals is:

Diagonals = 12(12-3)/2 = 54

5.Why do we divide by 2 in the diagonals formula?

We divide by 2 because each diagonal is counted twice, once from each endpoint.

Glossary for Diagonals Formula

  • Polygon: A closed geometric shape with straight sides.
  • Diagonal: A line segment connecting two non-adjacent vertices of a polygon.
  • Vertex: A point where two or more lines or edges meet.
  • Non-adjacent vertices: Vertices that are not next to each other in a polygon.
  • Hexagon: A six-sided polygon.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.