Thinking of what polygons are? In Euclidean geometry, a polygon is a crucial concept. Polygons are a closed plane figure in which all the sides are line segments. Each side should bisect exactly two other sides however only at their endpoints. The side of polygons should be noncollinear and must have a common endpoint. Having said that, there are different types of polygons and each polygon is generally named considering the number of sides it has. Note that a polygon having n-sides (=12) is called an n-gon.
Classic daily life polygon examples include the building which houses the US Department of Defense called pentagon because it has 5 sides.
Below is a clear depiction of polygons along with sides and illustrations of each.
Polygon Examples With Sides
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Types of Polygon
Based upon the sides and angles of a closed plane figure, we can classify the polygons into following different types, namely:
Types of Polygons and Its Properties
If all the sides and the interior angles of the polygon measure equal, then it is what we call a regular polygon. A regular polygon is a polygon which has all the sides and all the angles congruent. The examples of regular polygons include plane figures such as square, rhombus, equilateral triangle, etc.
In case of all the sides and the interior angles of the polygon do not measure similar, then it is called as an irregular polygon. Examples of irregular polygons include a rectangle, a kite, and a scalene triangle etc.
If one or more interior angles of a polygon measure more than 180°, then it is referred to as a concave polygon. A concave polygon can consist of a minimum of four sides. The vertex will point towards the interior of the polygon.
If all the interior angles of a polygon strictly measure less than 180°, then it is called a convex polygon. The vertex points outwards from the centermost of the shape.
Properties of Polygons
As already mentioned, polygons are classified depending upon their sides, shape, angle and properties. Thus, here we bring you the key properties of polygons that will help you to simply determine the types of polygons very easily.
Sum of all the interior angles of an n-sided polygon = (n – 2) × 180°.
The angle measurement of each interior angle of an n-sided regular polygon = [(n – 2) × 180°]/n.
The angle measurement of each exterior angle of an n-sided regular polygon = 360°/n.
Number of diagonals in a polygon having n sides = n(n – 3)/2.
Number of triangles formed by connecting the diagonals from one corner of a polygon = n – 2.
Introduction to Angles of Polygons
As we are already familiar, any polygon consists of as many vertices as its sides. In addition, each corner possesses a specific measure of angles. These angles are classified into two kinds of angles namely interior angles and exterior angles of a polygon.
Interior Angle Property of a Polygon
If we need to calculate the sum of all the interior angles of a simple n-gon, then we use the formula = (n − 2) × 180°.
Sum of all the interior angles formula = (n − 2) π radians.
In which ‘n’ is equivalent to the number of sides of a polygon.
For instance, a quadrilateral consists of four sides, thus, the sum of all the interior angle is given as:
Sum of interior angles of a 4-sided polygon i.e. a quadrilateral= (4 – 2) × 180°
= 2 × 180°
Exterior Angle Property of a Polygon
This property postulates that the sum of the interior, as well as the corresponding exterior angles at each vertex of any polygon, is supplementary to each other, meaning that will be equal to 180 degrees. That being said, for a polygon;
Interior angle + Exterior angle = 180°
Exterior angle = 180° – Interior angle
Area and Perimeter Formulas of Polygons
The area and perimeter of different types of polygons are dependent on the sides.
Area of a polygon is described as the region covered by the particular polygon in a 2D plane.
The perimeter of a polygon is defined as the total distance covered by the sides of a polygon.
There is also a seamless polygon triangle.
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