What Is A Ten Sided Shape Called In 2023?
Shapes are an essential part of mathematics, and they play a vital role in our daily lives. They are everywhere around us, from the basic geometric shapes we learned in school to the complex shapes we use in engineering and architecture. In this article, we will explore the world of ten-sided shapes, their properties, and what they are called.
What is a Ten Sided Shape?
Definition
A ten-sided shape is a polygon with ten sides, ten angles, and ten vertices. Polygons are closed plane figures that have straight sides and angles. They are classified according to the number of sides they have. A ten-sided polygon is called a decagon.
Properties of a Decagon
A decagon has ten sides of equal length and ten angles of equal measure. The sum of the interior angles of a decagon is 1440 degrees, and each angle measures 144 degrees. The exterior angle of a decagon measures 36 degrees. A decagon can be inscribed in a circle, and the sum of the exterior angles is always 360 degrees.
Types of Decagons
There are different types of decagons based on the length of their sides and the measure of their angles. Regular decagons have ten sides of equal length and angles of equal measure. Irregular decagons have ten sides of different lengths and angles of different measures. Convex decagons have all their angles pointing outwards, while concave decagons have at least one angle pointing inwards.
Real-Life Examples of Decagons
Decagons can be found in various structures around us. Some of the examples include:
- The shape of a soccer ball is a truncated icosahedron, which is made up of twenty regular hexagons and twelve regular decagons.
- The United States one-dollar coin has a regular decagon inscribed in it.
- The famous Stonehenge monument in England has ten-sided stones arranged in a circle.
How to Calculate the Properties of a Decagon?
Calculating the properties of a decagon can be challenging, but it is essential in fields such as geometry and engineering. The following are some of the formulas used to calculate the properties of a decagon:
- Formula for the sum of the interior angles of a decagon: (n-2) x 180 degrees, where n is the number of sides. For a decagon, n = 10, so the sum of the interior angles is (10-2) x 180 = 1440 degrees.
- Formula for the measure of each interior angle of a regular decagon: (n-2) x 180 / n degrees, where n is the number of sides. For a regular decagon, n = 10, so the measure of each interior angle is (10-2) x 180 / 10 = 144 degrees.
- Formula for the measure of each exterior angle of a regular decagon: 360 / n degrees, where n is the number of sides. For a regular decagon, n = 10, so the measure of each exterior angle is 360 / 10 = 36 degrees.
Conclusion
In conclusion, a ten-sided shape is called a decagon. It is a polygon with ten sides, ten angles, and ten vertices. Decagons have unique properties that make them useful in various fields. They can be regular or irregular and convex or concave. Understanding the properties of a decagon is essential in geometry and engineering, and it can help us appreciate the beauty of shapes in our daily lives.
So, the next time you see a ten-sided shape, remember that it is called a decagon!
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