Cuál Es El Decágono
If you're interested in geometry and shapes, you may have heard of the term "decágono." But what exactly is a decagon, and what are its properties? In this article, we'll explore the decagon in detail, from its definition to its various properties and applications.
Definition of Decagon
A decagon is a polygon with ten sides and ten angles. It is also known as a 10-gon. The word "decagon" comes from the Greek words "deka" (meaning ten) and "gonia" (meaning angle).
Like all polygons, a decagon is a closed figure with straight sides. Each of its ten sides connects two vertices (corners), and each of its ten angles is formed by three consecutive vertices. The sum of the interior angles of a decagon is 1440 degrees.
Types of Decagons
There are several types of decagons, based on their properties and characteristics. These include:
Regular Decagon
A regular decagon is a decagon with all sides and angles equal. It has ten lines of symmetry and can be inscribed in a circle. Its interior angles are each equal to 144 degrees.
Irregular Decagon
An irregular decagon is a decagon with sides and angles of different lengths and measures. It does not have any lines of symmetry and cannot be inscribed in a circle.
Convex Decagon
A convex decagon is a decagon in which each interior angle is less than 180 degrees. It does not have any "dents" or concave sections.
Concave Decagon
A concave decagon is a decagon in which at least one interior angle is greater than 180 degrees. It has one or more "dents" or concave sections.
Properties of Decagons
Decagons have several interesting properties, including:
Area
The area of a regular decagon can be found using the formula A = (5/4) × s² × √(5+2√5), where s is the length of one side. The area of an irregular decagon can be found by dividing it into triangles and adding up their areas.
Perimeter
The perimeter of a decagon can be found by adding up the lengths of its ten sides. For a regular decagon, the formula is P = 10s, where s is the length of one side. For an irregular decagon, the perimeter can be found by measuring each side separately.
Diagonals
A decagon has 35 diagonals, or lines that connect non-adjacent vertices. The formula to find the number of diagonals is n(n-3)/2, where n is the number of sides (in this case, 10).
Circumscribed Circle
A regular decagon can be inscribed in a circle, or circumscribed. The radius of this circle can be found using the formula r = s/2 × √(5+2√5), where s is the length of one side.
Applications of Decagons
Decagons have several applications and uses, including:
Architecture
Decagons can be found in architecture, particularly in the design of buildings, windows, and doorways. The regular decagon is often used in the design of Islamic art and architecture.
Jewelry
Decagons can also be found in jewelry, particularly in the design of pendants, earrings, and rings. The regular decagon is often used in the design of Celtic and other ethnic jewelry.
Mathematics
Decagons are used in mathematics as an example of a polygon with ten sides and ten angles. They are also used in geometry and trigonometry problems and proofs.
Conclusion
Overall, the decagon is a fascinating shape with many interesting properties and applications. Whether you're interested in architecture, jewelry, or mathematics, the decagon is a shape worth exploring and studying. So next time you come across a decagon, you'll have a better understanding of what it is and what it can do.
References:- https://www.mathsisfun.com/geometry/decagon.html
- https://www.sciencedirect.com/topics/mathematics/decagon
- https://en.wikipedia.org/wiki/Decagon
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