Have you ever wondered what a polygon is? You might have seen some shapes that look like polygons, such as squares, triangles, or stars. But what exactly makes a shape a polygon? In this article, we will explain what a polygon is, how to name different polygons, and show you some examples of polygons. By the end of this article, you will be able to identify polygons and impress your friends and teachers with your knowledge.
What is a Polygon?
A polygon is a two-dimensional shape that is made up of straight lines that connect to form a closed loop. The word “polygon” comes from two Greek words: “poly”, which means “many”, and “gon”, which means “sides”. So, a polygon is a shape with many sides.
The straight lines that make up a polygon are called the edges or sides of the polygon. The points where the edges meet are called the vertices or corners of the polygon. A polygon can have any number of sides and vertices, as long as they are straight and form a closed loop.
Here is an example of a polygon:
!polygon
This shape has four sides and four vertices, so it is a polygon.
How to Name Polygons
The way we identify different shapes with many straight edges, called polygons, is by the count of their sides. For example, a polygon with three sides is called a triangle, and a polygon with four sides is called a quadrilateral. Here are some common names for polygons based on the number of sides:
| Number of Sides | Name of Polygon |
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 9 | Nonagon |
| 10 | Decagon |
Some polygons have special names based on the length of their sides and the size of their angles. For example, a polygon with four equal sides and four equal angles is called a square, and a polygon with six equal sides and six equal angles is called a hexagon. These polygons are called regular polygons, because they are symmetrical and have the same shape on all sides. Here are some examples of regular polygons:
!Regular polygons
Types of Polygons
Polygons can be simple or self-intersecting. A simple polygon is one that does not cross over itself, except at the shared endpoints of consecutive edges. A simple polygon has only one boundary, and the inside and outside of the polygon are clearly defined. Here are some examples of simple polygons:
!simple polygons
A self-intersecting polygon is one that crosses over itself at some point, creating more than one boundary. A self-intersecting polygon does not have a clear inside and outside, and some parts of the polygon may overlap. Here are some examples of self-intersecting polygons:
!self-intersecting polygons
Why are Polygons Important?
Polygons are an important part of geometry, which is the study of shapes and their properties. Geometry helps us understand the world around us, and how to measure and compare different shapes and objects. Geometry also helps us create beautiful designs and patterns, such as art, architecture, and games.
Polygons are also fun to play with and explore. You can create your own polygons by drawing straight lines on a paper or a screen, and see what shapes you can make. You can also find polygons in nature, such as snowflakes, honeycombs, or flowers. You can also use polygons to make puzzles, such as tangrams, which are shapes that can be arranged to form different figures.
Conclusion
In this article, we learned what a polygon is, how to name different polygons, and saw some examples of polygons. We also learned that polygons can be simple or self-intersecting, and that polygons are important for geometry and fun. We hope you enjoyed this article and learned something new.
FAQS
What is a polygon?
A polygon is a closed two-dimensional shape that is made up of straight lines that connect to form a closed loop.
How many sides does a polygon have?
A polygon has at least three sides, but can have any number of sides. The number of sides determines the name of the polygon, such as triangle, quadrilateral, pentagon, etc.
What is the difference between a regular and an irregular polygon?
A regular polygon is a polygon that has all sides and angles equal, such as a square or a hexagon. An irregular polygon is a polygon that has different lengths of sides and/or different sizes of angles, such as a rectangle or a scalene triangle.
What is the difference between a convex and a concave polygon?
A convex polygon is a polygon that has all interior angles less than 180 degrees, and the vertices point outwards from the center of the shape. A concave polygon is a polygon that has one or more interior angles greater than 180 degrees, and some vertices point inwards towards the center of the shape.
How do you find the sum of the interior angles of a polygon?
The sum of the interior angles of a polygon can be found by using the formula: (n – 2) × 180°, where n is the number of sides of the polygon. For example, the sum of the interior angles of a pentagon is (5 – 2) × 180° = 540°.
How do you find the area of a polygon?
Q: A: The area of a polygon depends on the shape and the formula of the polygon. Some common formulas are:
Area of a triangle = ½ × base × height
Area of a rectangle = length × width
Area of a parallelogram = base × height
Area of a trapezoid = ½ × (sum of parallel sides) × height
Area of a regular polygon = ½ × perimeter × apothem
What are some examples of polygons in real life?
Q: A: Some examples of polygons in real life are:
The shape of a honeycomb is a hexagon
The shape of a stop sign is an octagon
The shape of a pizza slice is a triangle
The shape of a chessboard is a square
The shape of a snowflake is a star polygon