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Types of Polygons

Polygon is a closed two-dimensional figure that is made up of joining line segments together. Here, we shall discuss about types of polygons.

The classification of polygons is as follows:
There are two main types of polygons on the basis of sides and angles:

  • Regular Polygon
  • Irregular Polygon
Regular polygon is the one in which all the sides are equal and all the interior angles are equal.

Properties of a Regular Polygon
(1) Sum of all exterior angles of a regular polygon is $360^{\circ}$.
(2) Each exterior angle of a regular polygon measures $\frac{360^{\circ}}{n}$, where n is the number of sides.
(3) Sum of the interior and exterior angle at a point is $180^{\circ}$. Therefore, measure of each interior angle is given by:
Interior angle = $180^{\circ}$ - exterior angle.

= $180^{\circ} - $$\frac{360^{\circ}}{n}$

= $n \times $$\frac{180^{\circ}}{n}$$ - 2 \times $$\frac{180^{\circ}}{n}$

= (n - 2) $\frac{180^{\circ}}{n}$

Following diagram shows a regular polygon:
Regular Polygon

Irregular polygon is the one that is not regular, i.e. the polygon in which all side are not equal and all angles are not same, is known as an irregular polygon. Following images illustrates an irregular polygon:
Irregular Polygon

Polygons can be classified further on the basis on shapes
  • Convex Polygon
  • Concave Polygon
  • Complex Polygon
Convex polygon has all the vertices outwards. Each interior angle of a convex polynomial is less than $180^{\circ}$. An example of convex polygon is shown below:
Convex Polygon

Concave polygon has at least one vertex pointing inwards. At least one interior angle of a concave polynomial measures greater than $180^{\circ}$. An example of concave polygon is shown below:
Concave Polygon

Complex polygon is a polygon in which the one or more sides intersect the other. Complex polygon is an exception and breaks many rules which other types of polygons follow. An example of a complex polygon is a star polygon which demonstrated below:
Complex Polygon

Related Calculators
Polygon Calculator Area of a Polygon Calculator
Perimeter of a Polygon Calculator

More topics in  Types of Polygons
Convex Polygon Concave Polygon
Regular Polygon Irregular Polygon
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