Polygons

Look around you for Polygons. Did you notice that all objects around you have a shape? Some are flat shapes and some are solid. Can you recognize some of them? In this article, you will learn about a special group of flat or two-dimensional shapes called Polygons. Read on to find out more about the properties, classifications, hierarchy, formulae, and interesting games to understand them better.
Let us understand some basic geometrical objects before we define the Polygons.

Curve

A line that is traced on a plane without lifting the pen.

Closed curve

A curve that begins and ends at the same point.

Simple closed curve

A curve that does not intersect itself.

What are Polygons?

A polygon is a flat simple closed curve made up of only straight line segments. Each line segment forming the polygon is called a ‘Side.’ The name Polygons is a combination of two Greek words where ‘Poly’ means many and ‘Gons’ means sides. Hence, a two-dimensional shape with three or more sides is a polygon.
The number of sides of a polygon plays an important role in its nomenclature. A polygon is a Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, or Decagon, if the number of sides is 3, 4, 5, 6, 7, 8, 9, or 10 respectively. This process of naming the polygon taking the number of sides into account continues similarly for other polygons as well.
Give Nonagon and Decagon as well.

How are the Polygons classified?

Classification Type 1
Basically, they can be divided into two main groups based on the types of sides and angles.

Regular Polygons

A polygon having sides of equal lengths and angles of equal measure.

Irregular Polygons

A polygon that is not regular.
You can compare and get to know about the examples by looking at the image below.

Classification Type 2
If regular and irregular polygons are formed based on the types of attributes, we can also divide them based on just the angle measures.

Concave Polygons

Polygons in which at least one angle is more than 180 degrees.

Convex Polygons

Polygons in which every angle is less than 180 degrees.

Classification Type 3:
We have already come across the types of polygons based on the number of attributes while discussing their names. This can be considered as another method to divide them into groups.

Polygon Hierarchy

After forming groups of various types of polygons, we notice that some shapes are in various groups. And these groups or families contain more or fewer polygons when compared with others. This establishes a “Hierarchy of the Polygon classes.”
Let us understand how this family tree is established based on the classifications that were discussed so far.

The above image tells us that a Square has the same attributes as a rectangle but more specific ones.
Therefore, a square is also a rectangle!
This establishes the following hierarchy.

But, since squares and rectangles both have 4 sides, they belong to an even larger category called “Quadrilaterals.” Thus establishing the sub-family of polygons ‘The Quads,’ as we fascinatingly call it at beGalileo.

Similarly, this generation of different members of subclasses of the superset polygons can be continued in different ways and the picture below exemplifies this.

Properties of Polygons

They are always 2 Dimensional geometrical figures.

They are made of straight line segments.

Exterior angles

For a regular polygon of ‘n’ sides, we can calculate the measure of the exterior angles using the formula given below.

For a convex polygon of ‘n’ sides,
Sum of exterior angles = 4 right angles

Interior angles

For a regular polygon of ‘n’ sides,

Each interior angle = 1800 – each exterior angle
For a convex polygon of ‘n’ sides,
Sum of interior angles = (2n – 4) right angles

Number of diagonals in a polygon of ‘n’ sides = n(n-3)2

Math games for polygons

Here are some games that you can play in order to gain a better knowledge about them.

Polygon Sorting Cards

There are 26 polygons given in the image below. You need to sort the them into groups of figures with equal angles, equal sides and both. Write their numbers in the circles.

The Polygon Tangrams

Identify the polygons in the given tangrams. The one who finds the most of them is the winner. Remember to look beyond boundaries!

Real Life Example of Polygons

We have flat shapes everywhere. Therefore, they are everywhere around us. Where some occur naturally, while some others are man made.
Examples:

Castel De Monte

It is in Apulia, Italy, and was built more than 750 years ago. The fortress has one central building with eight surrounding towers. Can you identify the Polygon?

Honeycombs

The sides and base of each cell are likewise polygonal shapes, and the surface of the wax honeycomb formed by bees is composed of a variety of hexagons.

Applications of Polygons

A polygon is a basic shape in computer graphics or network analysis that is used for modeling and visualization.
Their importance would most likely be explained by the range of polygonal shapes frequently used in current architecture. The triangle is frequently utilised in construction due to its moderately robust shape
The rectangle is employed in many applications since our area of sight is essentially rectangular. For example, most televisions are rectangular to make watching more convenient and enjoyable. Phone screens and photo frames also fall in the same category.

Conclusion

This is a topic that is widely explored to even the current day by mathematicians. Many complex geometrical properties and theories are developed on the same basis by composing and decomposing many polygons. These are very useful in establishing new problem-solving techniques like the finite element methods, which in turn are applied to solve many real life scenarios. Now that you know about these fascinating geometrical shapes. Why don’t you go ahead and look around you again and play around with them?
Let’s become a polygon-might!