Which Polygon Has 11 Sides?
As geometric shapes, polygons have always fascinated mathematicians and students alike. One of the interesting aspects of polygons is the number of sides they have. In this article, we will explore the polygon with 11 sides and its properties.
What is a Polygon?
A polygon is a closed two-dimensional shape that has straight sides. The sides of a polygon are called edges, and the points where the edges meet are called vertices. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, and decagons.
What is an 11-Sided Polygon Called?
An 11-sided polygon is called an undecagon or hendecagon. The word "undecagon" comes from the Greek words "hendeka," which means "eleven," and "gon," which means "corner" or "angle."
Properties of an Undecagon
Like all polygons, an undecagon has certain properties that make it unique. Here are some of the properties of an undecagon:
- An undecagon has 11 sides, 11 vertices, and 11 interior angles.
- The sum of the interior angles of an undecagon is 1,440 degrees.
- The sum of the exterior angles of an undecagon is 360 degrees.
- An undecagon can be regular or irregular. A regular undecagon has sides of equal length and angles of equal measure.
Construction of an Undecagon
Constructing an undecagon is not as easy as constructing polygons with fewer sides. There are several methods for constructing an undecagon, but the most common method is using a compass and a straightedge.
Here are the steps to construct an undecagon:
- Draw a circle with the desired radius.
- Divide the circle into 11 equal parts using a protractor.
- Connect the points where the divisions intersect with the circle to form the sides of the undecagon.
Real-Life Examples of Undecagons
Undecagons are not commonly found in everyday life, but they can be seen in some architectural designs and art. One example of an undecagon in architecture is the Undecagonal Tower in England. This tower has 11 sides and is located in the city of Bristol.
Other Interesting Facts About Undecagons
Here are some other interesting facts about undecagons:
- The undecagon is the 11th polygon in the sequence of regular polygons.
- The undecagon is not a constructible polygon with a compass and straightedge alone.
- The undecagon has a Schläfli symbol of {11}.
Conclusion
In conclusion, the undecagon is a unique and interesting polygon with 11 sides. While it may not be as commonly found as other polygons, its properties and construction methods make it a fascinating shape to study. Whether you are a student learning about polygons or a mathematician exploring geometric shapes, the undecagon is worth exploring further.
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