Polygon - Definition & Properties

A polygon is defined in geometry as any closed curve composed of a set of line segments (sides) connected so that no two segments cross. 

Triangles (three sides), quadrilaterals (four sides), and pentagons are the simplest polygons (five sides). 

If none of the sides intersect the polygon when extended, it is convex; otherwise, it is concave. 

An equilateral polygon is one with equal sides on all sides. Equiangular is defined as having all interior angles equal. 

A regular polygon is any polygon that is both equilateral and equiangular (e.g., equilateral triangle, square).

What Are Polygons?

Polygons are two-dimensional geometric figures with a fixed number of sides. A polygon's sides are made up of straight-line segments that are joined end to end. 

A polygon's line segments are referred to as its sides or edges. The point at which two line segments intersect is referred to as the vertex or corners, and an angle is formed as a result. A triangle with three sides is an example of a polygon.

A circle is also a plane figure, but it is not considered a polygon because it is curved and lacks sides and angles. 

As a result, we can say that all polygons are 2d shapes, but not all two-dimensional figures are polygons.

Properties Of Polygon

1. The sum of the interior angles of all the quadrangles equals 360°, which is one of the polygon's important properties.

 

2. A simple polygon is one that does not cross over itself and has only one boundary. It is otherwise a complex polygon.

Polygonal Shapes

We can classify polygons into several types based on their sides and angles, namely:

• Polygon with Regular Shapes
• Polygon with Irregular Shapes
• Polygon that is convex
• Polygon that is concave

1. Polygon with Regular Shapes

A polygon in which all of the sides and interior angles of the polygon are equal is known as regular polygon. Regular polygons include squares, rhombuses, equilateral triangles, and so on.

2. Polygon With Irregular Shapes

An irregular polygon is one in which all of the sides and interior angles of the polygon are of different lengths. For example, a scalene triangle, a rectangle, a kite, and so on.

3. Convex Polygon 

A polygon in which all of the interior angles are strictly less than 180 degrees is known as a convex polygon. The vertex will extend from the centre of the shape.

4. Concave Polygon

A polygon that has one or more interior angles that are greater than 180 degrees is called a concave polygon. 

A concave polygon can have a minimum of four sides. The vertex is pointing inside the polygon.

A number of polygons, however, are defined based on the number of sides, angles, and properties. 

Polygonal Applications In Real Life

Geometry requires an understanding of shapes. Shapes can be used in a variety of real-world applications.

• The tiles you walk on are square, indicating that they are polygons.
• The truss of a building or bridge, the walls of a building, and so on are examples of polygons. Trusses are triangular in shape, whereas walls are rectangular.
• A polygon is the rectangular part of a chair in which you and your family members are sitting.
• A polygon is a rectangular-shaped screen on your laptop, television, or mobile phone.
• A polygon is something like a rectangular football field or playground.

Cuemath

You've probably noticed that the subject is simple to grasp. Solving a problem involving polygons will not feel like a problem if you have conceptual clarity on the subject, which is where cuemath comes in. 

Cuemath is the most effective online math services platform for establishing a solid mathematical foundation. Go to the Cuemath website to learn more about these concepts in depth.