Polygon is a generic shape in the world of geometry that has at least three non-aligned line segments. In simple words, imagine a shape that has at least three vertices and lines. A polygon has many components and each component is very important for you to understand. That is why we dedicated this resource to components of a polygon. Furthermore, we will also talk about the types of polygons in this resource as well.
Components of a Polygon
A polygon has sides and angles as primary components. From the sides and angles, we can figure out other components as well such as vertices, diagonal, angles, and area and perimeter. Although each component of a polygon should be discussed in detail. Hence, we will give you a brief introduction of them here but if you want to learn more about them, click on the link.
There are no fixed sides of a polygon and that makes it more special and interesting to learn. Polygons are given their name according to their sides, take an example of a hexagon. The word hex is a Greek word that means "six" and a hexagon has six sides too. Do you see a pattern? The first word is usually the Greek word which is telling you the side and the last word, "gon", came from the word "polygon". However, there are some exceptions, take an example of the triangle, there is no Greek word in it neither it has "gon" in its end. There are some exceptions, not just triangle, rectangle, rhombus, parallelogram, and many more. However, this exception is till the four-sided polygon, the rest polygon fells into the same pattern.
Of course, where there are sides, there are vertices. A vertex is formed when two straight line meets at a point. When a vertex is formed, we usually represent the lines as the arms. A simple polygon will always have at least three vertices, which will enclose an area making it a polygon. Yes, this also means that a polygon can have more than twenty vertices. You will also note that there will be a deflection from one arm to another. We call that deflection an angle. Angles are the result of a vertex, but then what is an angle?
As mentioned above, an angle is the result of a vertex. Angle is the measurement of the deflection of one arm from another arm. Angles is also a keen interest of many mathematicians. Polygons have many types of angles such as acute angles, right angles, supplementary angles, adjacent angles, and the list goes on and on.
A diagonal of a polygon is a line segment that joins two non-consecutive vertices. Triangle is the only exception. In simple words, a triangle is the only polygon that doesn't have a diagonal. Diagonals are formed because of vertices and when you join two vertices are not adjacent, which means you are drawing a diagonal. A diagonal is not a side of a polygon! Never ever confuse a diagonal with a side.
Area and Perimeter
When you join all lines, creating vertices, you made a polygon. Ever thought about what is inside of a polygon? We call it an area if you are working in a 2-dimensional region. The area is the region occupied inside of a boundary and the perimeter is the length of the boundary. Consider a square, it has four sides and each side is equal. The area would be the region inside of the four sides and the perimeter would be the sum of all four sides.
The word, "convex", means that all of the interior angles are less than . Therefore, for a convex polygon, all of its angles are less than . In addition, all of the diagonals are internal.
Concave is the opposite of convex. It means that all of the interior angles are more than . Therefore, for a concave polygon, all of its angles are more than . In addition, at least one of the diagonals is outside the shape of the polygon.
In an equilateral polygon, all sides are equal in length.
In an equiangular polygon, all angles are equal.
A regular polygon has both, equal sides and equal angles.
An irregular polygon doesn't have equal angles nor equal sides.
Polygons are categorized according to their sides with some exceptions. These sides gave them a new name and a new shape and a new shape means new properties. There are so many polygons, distinguished according to their sizes, that we can't cover it in a single resource. Click on the link to learn about different types of polygon by their sides.
The platform that connects tutors and students