102 LearnersLast updated on August 9th, 2025
Math Formula for Diagonals
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.
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.
Mistake 1
Forgetting to Divide by 2
Students sometimes forget to divide the product by 2, leading to incorrect results. Always remember that each diagonal is counted twice, so you must divide by 2.
Mistake 2
Misinterpreting n as Edges Instead of Sides
Students may confuse the number of edges with the number of sides. Ensure that n represents the number of sides of the polygon.
Mistake 3
Applying the Formula to Non-Polygons
The formula is only applicable to polygons. Ensure that the shape in question is a polygon before applying the formula.
Mistake 4
Ignoring the Concept of Non-Adjacent Vertices
The formula is based on connecting non-adjacent vertices. Make sure to understand this concept to correctly apply the formula.
Examples of Problems Using the Diagonals Formula
Problem 1
How many diagonals are there in an octagon?
There are 20 diagonals in an octagon.
Explanation
Using the formula:
Diagonals = 8(8-3)/2 = 20
Problem 2
Find the number of diagonals in a decagon.
A decagon has 35 diagonals.
Explanation
Using the formula:
Diagonals = 10(10-3)/2 = 35
Problem 3
Calculate the number of diagonals in a heptagon.
There are 14 diagonals in a heptagon.
Explanation
Using the formula:
Diagonals = 7(7-3)/2 = 14
FAQs on Diagonals Formula
1.What is the formula for the number of diagonals in a polygon?
2.Can the diagonals formula be applied to any shape?
3.What is the significance of the diagonals formula?
4.How do you calculate the number of diagonals in a dodecagon?
5.Why do we divide by 2 in the diagonals formula?
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.
