Polygon All Methods is the topic of International GCSE, O level Mathematics (Specification B) Geometry. We will be covering all math topics gradually.
Polygon All Methods
What are Polygons?
A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides).
A minimum of three line segments is required to connect end to end, to make a closed figure. Thus a polygon with a minimum of three sides is known as Triangle and it is also called 3-gon. An n-sided polygon is called n-gon.
Polygon shape
By definition, we know that the polygon is made up of line segments. Below are the shapes of some polygons that are enclosed by the different number of line segments.
Types of Polygon
Depending on the sides and angles, the polygons are classified into different types, namely:
- Regular Polygon
- Irregular Polygon
- Convex Polygon
- Concave polygon
Regular Polygon
If all the sides and interior angles of the polygon are equal, then it is known as a regular polygon. The examples of regular polygons are square, equilateral triangle, etc.
Irregular Polygon
If all the sides and the interior angles of the polygon are of different measure, then it is known as an irregular polygon. For example, a scalene triangle, a rectangle, a kite, etc.
Convex Polygon
If all the interior angles of a polygon are strictly less than 180 degrees, then it is known as a convex polygon. The vertex will point outwards from the centre of the shape.
Concave Polygon
If one or more interior angles of a polygon are more than 180 degrees, then it is known as a concave polygon. A concave polygon can have at least four sides. The vertex points towards the inside of the polygon.
However, a number of polygons are defined based on the number of sides, angles and properties.
Angles of Polygon
As we know, any polygon has as many vertices as it has sides. Each corner has a certain measure of angles. These angles are categorized into two types namely interior angles and exterior angles of a polygon.
Interior Angle Property
The sum of all the interior angles of a simple n-gon = (n − 2) × 180°
Or
Sum = (n − 2)π radians
Where ‘n’ is equal to the number of sides of a polygon.
For example, a quadrilateral has four sides, therefore, the sum of all the interior angles is given by:
Sum of interior angles of 4-sided polygon = (4 – 2) × 180°
= 2 × 180°
= 360°
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