How Many Diagonals Are There In A Regular Hexagon?

September 02, 2024 Posting Komentar

What is a Diagonal, Definition, Examples, Facts & Formula Cuemath from www.cuemath.com

Welcome to our article where we will be discussing the number of diagonals in a regular hexagon. A hexagon is a six-sided polygon, and a regular hexagon is a shape where all the sides and angles are equal. Diagonals are lines that connect non-adjacent vertices of a polygon. In this article, we will explore the formula to calculate the number of diagonals in a regular hexagon and provide examples to help you better understand the concept.

Formula to Calculate the Number of Diagonals in a Regular Hexagon

The formula to calculate the number of diagonals in a regular hexagon is:

n(n-3)/2

Where n is the number of sides in the polygon. In the case of a hexagon, n=6.

Substituting the value of n in the formula:

6(6-3)/2 = 9

Therefore, there are 9 diagonals in a regular hexagon.

Explanation of the Formula

The formula to calculate the number of diagonals in a regular polygon is derived by using the combination formula. In a polygon with n sides, there are n vertices. To create a diagonal, we need to choose two vertices that are not adjacent. Since there are n vertices, the number of ways to choose two vertices is:

nC2 = n(n-1)/2

However, this formula counts the sides of the polygon as diagonals too, which is not correct. In a regular polygon, all the sides are equal, and we can choose any vertex as the starting point. Therefore, we need to subtract n from the above formula to get the correct number of diagonals:

n(n-1)/2 - n = n(n-3)/2

Examples

Let's take a regular hexagon and draw all the possible diagonals:

Regular hexagon with all diagonals

As you can see, there are 9 diagonals in a regular hexagon:

Let's take another example. Suppose we want to find the number of diagonals in a regular octagon:

Substituting the value of n in the formula:

8(8-3)/2 = 20

Therefore, there are 20 diagonals in a regular octagon.

Conclusion

In conclusion, a regular hexagon has 9 diagonals. The formula to calculate the number of diagonals in a regular polygon is n(n-3)/2, where n is the number of sides in the polygon. We hope this article has helped you understand the concept of diagonals in a regular hexagon and how to calculate their number using the formula. If you have any questions or suggestions, please feel free to leave a comment below.