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A Comprehensive Guide To A Polygon With 10 Sides And 10 Angles

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Decagon Picture Images of Shapes
Decagon Picture Images of Shapes from kidsmathgamesonline.com

Geometry is an interesting subject that deals with the study of shapes, sizes, and positions of objects. One of the important topics in geometry is polygons. A polygon is a closed geometric figure with straight sides. In this article, we will be discussing a polygon with 10 sides and 10 angles.

What is a Polygon with 10 Sides and 10 Angles?

A polygon with 10 sides and 10 angles is called a decagon. The term decagon is derived from the Greek words "deca" meaning ten and "gonia" meaning angles. It is a two-dimensional shape that has 10 straight sides and 10 angles. Each angle measures 144 degrees, and the sum of all the angles in a decagon is 1440 degrees.

Properties of a Decagon

Like any other polygon, a decagon has its unique set of properties that make it distinctive. Here are some of the essential properties of a decagon:

  • A decagon has 10 straight sides of equal length.
  • A decagon has 10 internal angles of equal measure, i.e., 144 degrees each.
  • The sum of all internal angles in a decagon is 1440 degrees.
  • A decagon has 35 diagonals, i.e., straight lines connecting any two non-adjacent vertices.
  • The diagonals of a decagon intersect at 35 points inside the decagon.

Formulas for a Decagon

Some of the fundamental formulas related to a decagon are:

  • The total number of diagonals in a decagon = n(n-3)/2 = 35
  • The sum of all internal angles in a decagon = (n-2) x 180 = 1440 degrees
  • The measure of each internal angle in a decagon = (n-2) x 180/n = 144 degrees
  • The area of a decagon = (5/4) x (s^2) x (sqrt(5+2sqrt(5))) where s is the length of each side.

Types of Decagons

There are two types of decagons – regular and irregular decagons.

Regular Decagon

A regular decagon is a decagon with all sides and angles of equal length and measure, respectively. It has rotational symmetry of order 10, which means it can be rotated by multiples of 36 degrees to coincide with its original position. A regular decagon can be constructed using a compass and straightedge.

Irregular Decagon

An irregular decagon is a decagon with sides and angles of different lengths and measures. It does not have any rotational symmetry, and it cannot be constructed using a compass and straightedge.

Examples of Decagons in Real Life

Decagons can be found in several real-life objects, including:

  • The shape of a soccer ball is a combination of 12 regular pentagons and 20 regular hexagons, including 32 total faces. Each pentagon and hexagon in a soccer ball is a decagon with its vertices truncated.
  • The top of the United States Department of Agriculture building in Washington D.C., USA, is a regular decagon.
  • The inner ring of the Olympic flag has 10 interlocking rings that represent each of the ten participating nations in the first Olympic Games held in Athens, Greece, in 1896.

Conclusion

Decagons are fascinating geometric shapes with unique properties and formulas. Whether you are a math enthusiast or just curious about shapes, the decagon is worth exploring. Understanding decagons and other polygons can help you appreciate the beauty and complexity of geometry and its application in real-life scenarios.

So, go ahead and explore the world of decagons!

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