What Is A 10 Sided Polygon?

10sided Polygon ClipArt ETC from etc.usf.edu

When it comes to geometry, polygons are one of the most fundamental shapes. They are two-dimensional shapes that are made up of straight lines and angles. You might be familiar with some common polygons such as triangles, squares, and pentagons. But have you ever heard of a 10 sided polygon? In this article, we will explore what a 10 sided polygon is and some interesting facts about it.

What is a Polygon?

Before we dive into the details of a 10 sided polygon, let's first understand what a polygon is. A polygon is a closed shape that has three or more straight sides. The sides of a polygon do not cross each other, and the angles between the sides are always less than 180 degrees. Polygons can be regular or irregular, convex or concave, and can have any number of sides.

What is a 10 Sided Polygon Called?

A 10 sided polygon is called a decagon. The word "decagon" comes from the Greek word "deka" which means ten and "gonia" which means angle. A decagon has ten sides and ten angles. All the angles of a decagon add up to 1440 degrees, and each angle measures 144 degrees.

Types of Decagons

Decagons can be regular or irregular. A regular decagon has ten equal sides and ten equal angles. An irregular decagon has sides and angles of different lengths and measurements. In addition to this, a decagon can be convex or concave. A convex decagon has all its interior angles less than 180 degrees and all its vertices pointing outwards. A concave decagon has at least one interior angle greater than 180 degrees and at least one vertex pointing inward.

Properties of a Decagon

Let's take a closer look at the properties of a decagon:

A decagon has ten sides.

All the sides of a regular decagon are equal in length.

All the angles of a regular decagon are equal in measurement.

The sum of all the interior angles of a decagon is 1440 degrees.

The measure of each interior angle of a decagon is 144 degrees.

A decagon can be either convex or concave.

Real Life Examples of Decagons

Decagons can be found in many real-life objects and structures. For example:

The shape of a soccer ball is a truncated icosahedron, which is made up of 20 regular hexagons and 12 regular pentagons. Each hexagon and pentagon is a decagon.

The United States one-cent coin, commonly known as a penny, has a regular decagon shape on the back side.

The United States Department of Defense building, also known as The Pentagon, is a five-story building with five sides, each of which is a regular decagon.

How to Calculate the Area of a Decagon

The formula to calculate the area of a regular decagon is:

Area = (5/4) x (s^2) x (tan(π/10))

Where s is the length of one side of the decagon. To calculate the area of an irregular decagon, you need to split it into triangles, calculate the area of each triangle, and then add up the areas of all the triangles.

Conclusion

Decagons are fascinating shapes with unique properties. They have ten sides and ten angles, and can be regular or irregular, convex or concave. Decagons can be found in many real-life objects and structures, such as soccer balls, coins, and buildings. Knowing what a decagon is and its properties can help you better understand geometry and appreciate the shapes that surround us.

So, the next time you come across a decagon, you will know what it is and what it's called.

Source: etc.usf.edu

Source: etc.usf.edu

Source: etc.usf.edu