How Many Diagonals Does A Decagon Have?
Decagon is a polygon with ten sides and ten angles. It is a popular shape used in geometry and mathematics. If you are wondering how many diagonals a decagon has, then you have come to the right place. In this article, we will discuss the formula to calculate the number of diagonals in a decagon and how you can use it to solve related problems.
Formula to Calculate Diagonals in a Decagon
Before we dive into the formula, let's understand what a diagonal is. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. In a decagon, each vertex is connected to three other vertices by sides. Therefore, the total number of line segments connecting all the vertices of a decagon is:
n(n-3)/2
Where n is the number of sides of the polygon. In the case of a decagon, n is 10. Therefore, the formula to calculate the number of diagonals in a decagon is:
10(10-3)/2 = 35
So, a decagon has 35 diagonals.
Understanding the Formula
Now that we have the formula to calculate the number of diagonals in a decagon, let's understand how it works. The formula is based on the fact that each vertex of a polygon is connected to every other vertex except for the adjacent ones. In a decagon, each vertex is connected to three other vertices by sides. Therefore, to calculate the total number of line segments connecting all the vertices of a decagon, we need to subtract the number of sides and then divide the result by two.
So, the formula becomes:
n(n-3)/2
where n is the number of sides of the polygon.
Examples
Let's take some examples to understand the formula better.
Example 1:
Find the number of diagonals in a hexagon.
Solution:
Using the formula, we get:
6(6-3)/2 = 9
Therefore, a hexagon has 9 diagonals.
Example 2:
Find the number of diagonals in an octagon.
Solution:
Using the formula, we get:
8(8-3)/2 = 20
Therefore, an octagon has 20 diagonals.
Conclusion
In conclusion, a decagon has 35 diagonals. The formula to calculate the number of diagonals in a decagon is n(n-3)/2, where n is the number of sides of the polygon. We can use this formula to calculate the number of diagonals in any polygon with n sides. Understanding the formula and solving related problems will help you in your geometry and mathematics studies.
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