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Dodecagon: A 12-Sided Polygon Explained

CEO Khai Intela
Introduction Have you ever wondered about the different types of polygons? In geometry, a polygon is a two-dimensional closed geometric figure with a finite number of sides. You may be familiar with shapes like triangles...

Introduction

Have you ever wondered about the different types of polygons? In geometry, a polygon is a two-dimensional closed geometric figure with a finite number of sides. You may be familiar with shapes like triangles and quadrilaterals, but there's one particular polygon that we're going to explore in this article: the dodecagon.

What is a Dodecagon?

A dodecagon is a polygon with 12 sides. It also has 12 vertices and 12 interior angles. In other words, it's a twelve-sided shape that can be found in various real-life objects. Let's take a closer look at this fascinating polygon!

Dodecagon Image source: Saigon Intela

Types of Dodecagons

Dodecagons can be classified into different types based on their side lengths and angle measures. There are two main categories: regular dodecagons and irregular dodecagons.

Regular and Irregular Dodecagons

A regular dodecagon has sides and interior angles that are all equal in measure. The vertices of this polygon are evenly spaced around a circle. Each interior angle of a regular dodecagon measures 150 degrees.

On the other hand, an irregular dodecagon has sides that are not identical. The angles of this polygon may also vary. Due to its asymmetrical pattern, irregular dodecagons exhibit unique properties and characteristics.

Regular v. irregular dodecagon Image source: Saigon Intela

Concave and Convex Dodecagon

Another way to classify dodecagons is based on their interior angles. A concave dodecagon has at least one interior angle greater than 180 degrees. This causes some of its vertices to point towards the center.

On the other hand, a convex dodecagon has all interior angles less than 180 degrees. In a convex dodecagon, none of the vertices point towards the center.

Concave and convex dodecagon Image source: Saigon Intela

Now that we've explored the different types of dodecagons, let's dive deeper into their properties, area, and perimeter.

Properties of a Dodecagon

A dodecagon is a polygon with 12 sides, 12 angles, and 12 vertices. Let's take a closer look at its properties:

Interior and Exterior Angles

The sum of the interior angles of a polygon can be calculated using the formula $(n-2) \times 360°$, where n is the number of sides. For a dodecagon, which has 12 sides, the sum of the interior angles is 1800 degrees.

In a regular dodecagon, each interior angle is equal to 150 degrees. The sum of all the exterior angles of a regular dodecagon is 360 degrees.

Interior and exterior angle of dodecagon Image source: Saigon Intela

Diagonals of a Dodecagon

The number of diagonals in a polygon can be calculated using the formula $\frac{n(n-3)}{2}$, where n is the number of sides. For a dodecagon, there are 54 diagonals.

Triangles in a Dodecagon

The number of triangles formed by diagonals from every vertex of a dodecagon can be calculated using the formula $(n-2)$. In the case of a dodecagon, there are 10 triangles.

Area of a Dodecagon

The area of a dodecagon represents the total space covered by its boundaries. For a regular dodecagon, the area can be calculated using the formula $3 \times (2 + \sqrt{3}) \times s^2$, where s is the length of its side.

Perimeter of a Dodecagon

The perimeter of a dodecagon is the sum of all its sides. For a regular dodecagon, the perimeter can be calculated by multiplying the length of one side by 12.

Conclusion

Polygons are fascinating shapes with different properties and characteristics. Among them, the dodecagon stands out with its unique 12-sided structure. Understanding the concept of dodecagons and their various types can help us appreciate the complexity of two-dimensional shapes in our everyday lives.

Practice Problems and Frequently Asked Questions have been omitted for brevity.

Now that you know more about dodecagons, you can explore the world of polygons with confidence and curiosity. Embrace the beauty of geometry and the wonders it holds!

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