Polygons are the elementary shapes that create the framework of more difficult structures. From the simple triangle in mathematics to the figures in difficult constructions in actual life, polygons are everywhere. The word polygon has been derived from the Greek words poly, meaning many, and gon, means angles. Thus, it can be concluded that a polygon is a figure with many angles. It is a superficial, ended geometric structure created by the convergence of unlimited numbers of a horizontal line segments linked one after the other. The line segments in the polygon are known as the sides, while the tip where the lines connect is known as the vertex. The confined area inside the line segments makes the inside of the polygon; alternatively, the joining sides make the boundary of the shape. Each polygon consists of particular characteristics such as diagonals, interior and exterior angles , etc. The names of the polygons are as follows 3 sided polygon triangle, 4 sided polygon quadrilateral, 5 sided polygon pentagon, 6 sided polygon hexagon, 7 sided polygon heptagon, 8 sided polygon octagon, 9 sided polygon nonagon and 10 sided polygon decagon.
Attributes of A Polygon
Each polygon, in any case of its shape and number of sides displace particular attributes. These attributes of a polygon aid in describing and understanding the shapes correspondingly. Some of these attributes are as follows:
a) Closed Shape: Every polygon is a fixed shape, such that it's sides make a continuous cycle.
b) Straight sides: In polygons, the sides are made by horizontal line segments, not arcs.
c) Number of sides, angles and vertices: If a polygon has "x" number of sides, then the number of vertices and inside the angles will also be "x".
d) No crossing or overlapping sides: The line segments only bisect in their ends, meaning they neither meet nor converge other sides.
Types of polygons
Polygons can be divided into four wide segments: concave polygon, convex polygon, regular polygon and irregular polygon. Each of these types of polygons aid in understanding their particular attributes.
Convex Polygon : A convex polygon is a polygon where all the inside angles are less than 180 degrees and none of the vertices appear inward. If the two tips are linked in the polygon , it will always be inside the shape. Examples of convex polygon are equilateral triangle, rectangles and regular polygons.
Concave polygon: A concave polygon will have atleast one interior angle above 180 degrees, and atleast one vertex will appear to cave in towards the inside . Some diagonals will lie externally towards the polygon. Example of concave polygon are an arrowhead shaped quadrilateral and a star shaped polygon.
Regular Polygon: A regular polygon includes sides that are similar and all the interior angles are equal in measure. It's always convex in nature. This type of polygon has high consistency and equal angles. For example,a square, a equilateral triangle , a regular pentagon, etc.
Irregular Polygons: An irregular polygon is not similar in all sides or angles. These polygons can be less than 180 degrees or more than 180 degrees depending on the placement of the sides and angles. For example, a trapezium and a scalene triangle.
Interior and Exterior Angles of Polygons
Though having different attributes, each polygon experience particular similar polygon formulas for its diverse elements. An interior angle is created by bisecting the two adjacent sides inside the polygon. The sum of all the angles of any polygon can be calculated using the formula:
(Sides of polygon-2)*180 degree
In regular polygon the system of each interior angle is calculated by
{(Sides of Polygon-2)*180 degree}/Sides of the polygon
An external angle is made when one side of the polygon is extended, and the angle is made between the extended side and the following side. The sum of the interior and the transmitting exterior angles is 180 degrees, whereas the sum of the exterior angles is 360 degree.
Exterior angle= (360/ number of sides)
Diagonals In a Polygon
A diagonal is a line joining two adjacent vertices of a polygon. Polygons with more than three sides have diagonal .
Number of diagonal = {Side of polygon (Sides of polygon-3)/2}
