What Polygon Has 35 Diagonals?
Are you a math enthusiast looking for a new challenge? Or maybe you're just curious about polygons and their properties. Either way, you've come to the right place. In this article, we will explore the answer to the question, "What polygon has 35 diagonals?" Get ready to dive into the fascinating world of geometry.
Polygon Diagonals – What Are They?
Before we get to the specific polygon that has 35 diagonals, let's first define what a diagonal is. In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon. In other words, it's a line that goes through the interior of the polygon and doesn't touch any of its sides.
For example, in a triangle, there are no diagonals since all vertices are adjacent to each other. However, in a quadrilateral (a polygon with four sides), there are two diagonals connecting opposite vertices.
The Formula for Counting Diagonals
Now that we know what a diagonal is, let's talk about how to count them. The formula for finding the number of diagonals in a polygon is:
D = n(n-3)/2
Where D is the number of diagonals and n is the number of sides of the polygon. For example, in a pentagon (a polygon with five sides), we can plug in n=5 and get:
D = 5(5-3)/2 = 5
So a pentagon has 5 diagonals.
Which Polygon Has 35 Diagonals?
Now, let's answer the main question. Which polygon has 35 diagonals? To find out, we need to solve the formula for n when D=35:
35 = n(n-3)/2
After a bit of algebra, we get:
n^2 - 3n - 140 = 0
This is a quadratic equation that can be solved using the quadratic formula:
n = (3 ± √(3^2 + 4*1*140))/2
n = (3 ± 19)/2
n = 11 or n = -16
Since a polygon cannot have negative sides, we discard n=-16 and conclude that the polygon with 35 diagonals has 11 sides. This polygon is called an hendecagon or 11-gon.
Properties of an Hendecagon
Now that we know what polygon has 35 diagonals, let's explore some of its properties. An hendecagon has:
As you can see, an hendecagon is a complex and fascinating shape with many interesting properties.
Conclusion
In conclusion, we have answered the question, "What polygon has 35 diagonals?" We have learned that an hendecagon, or 11-gon, is the polygon with this property. We have also explored the formula for counting diagonals in a polygon and discovered some of the interesting properties of an hendecagon. I hope this article has sparked your interest in geometry and inspired you to explore more of its wonders.
Remember, math is not just about finding the right answer, but also about the journey of discovery and exploration.
Posting Komentar untuk "What Polygon Has 35 Diagonals?"