How Many Vertices Are There In A Decagon?
Decagon is a polygon with ten sides and ten angles. It is a fascinating geometric shape that has intrigued mathematicians for centuries. The decagon is a popular shape in architecture, art, and design. It is essential to know the number of vertices in a decagon to understand its properties and characteristics. In this article, we will explore the answer to the question, how many vertices are there in a decagon?
What is a Vertex?
Before we dive into the number of vertices in a decagon, let's define what a vertex is. A vertex is a point where two or more lines meet. In geometry, vertices are commonly used to define the corners of polygons, where two or more sides meet. The plural of vertex is vertices.
How to Find the Number of Vertices in a Decagon?
To find the number of vertices in a decagon, we need to know the definition of a vertex and the formula to calculate it. A decagon has ten sides and ten angles, which means it has ten vertices. The formula to calculate the number of vertices in a polygon is V = S + 2 - N, where V is the number of vertices, S is the number of sides, and N is the number of diagonals. For a decagon, the formula is V = 10 + 2 - 35 = 10.
Properties of a Decagon
A decagon has several unique properties that make it an intriguing geometric shape. Here are some of the essential properties of a decagon:
- A decagon has ten sides.
- A decagon has ten angles.
- The sum of the interior angles of a decagon is 1440 degrees.
- The sum of the exterior angles of a decagon is 360 degrees.
- A decagon has ten diagonals.
- A regular decagon has all sides and angles equal.
- A decagon can be inscribed in a circle.
- The area of a decagon can be calculated using the formula A = (5/4) x s^2 x √(5 + 2√5), where s is the length of a side.
Examples of Decagons
Decagons are prevalent in architecture, art, and design. Here are some examples of decagons:
- The United States Department of Defense building in Washington, D.C., has a decagon shape.
- The ancient Greek coins featured a decagon shape.
- The decagonal prism is a three-dimensional shape with a decagon as its base.
- The decagon is a popular shape in quilting patterns.
Fun Facts About Decagons
Here are some fun facts about decagons:
- The word "decagon" comes from the Greek words "deka," which means ten, and "gonia," which means angle.
- A decagon can be divided into seven triangles.
- A decagon can be used to construct a regular pentagon.
- A decagon can be used to construct a regular hexagon.
Conclusion
In conclusion, a decagon is a polygon with ten sides and ten angles. It has ten vertices, which can be calculated using the formula V = S + 2 - N. A decagon has several unique properties, such as having ten sides, ten angles, and ten diagonals. It is a popular shape in architecture, art, and design. Knowing the number of vertices in a decagon is essential to understand its properties and characteristics.
So, the next time you come across a decagon, you will know that it has ten vertices.
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