A polygon is a part of a plane bounded by a closed, broken, curved line. A polygon that equals all sides and angles is called a regular polygon. With the help of our calculator, you will learn how to calculate the area of a regular polygon. 

What Is a Polygon?

The figure below shows a closed broken line ABCDEF. This closed broken line is formed by 6 lines that are also its sides. Points from A to F are the vertices of the closed fracture line ABCDEF.

A closed broken line whose non-adjacent pages have no common points is called a simple closed broken line.

A simple closed broken line is called a polygonal line. A polygonal line divides a plane into two separate areas: inner and outer. The union of a polygonal line and its internal space is called a polygon.

Types Of Polygons

A polygon is a geometric figure in a plane bounded by a closed broken line. It has at least three pages and the same number of angles. A polygon can be convex or non-convex (concave).

At a convex angle, the line joining the two points of the broken line does not intersect any of its sides. In a non-convex polygon, the line joining the two points of the broken line intersects at least one of its sides.

Also, a polygon can be regular or irregular. A polygon is regular if all its sides are equal in length and angles are equal. An irregular polygon has unequal sides and angles.

Area of a regular polygon formula

A polygon is a two-dimensional shape with a finite number of straight sides. All polygons can be described by their number of sides and their angles. This calculator includes the area of regular polygon formulas, so you can find the size of any regular polygon with just a few simple calculations.

We can say that the area of a regular polygon is equal to one-half of the product of its Apothem and its Perimeter. The formula is given below: 

A = \frac{1}{4}\cdot n\cdot a^{2}\cdot cot(\frac{\pi }{n})

Perimeter is equal to the number of sides multiplied by side length.

How to calculate the area of a polygon

Suppose you are trying to find the area of a polygon. You can do it with our calculator easily. You need to have the next set of data:

Number of sides n 
– Side length a
Circumradius R – a radius of the circle inside which the polygon can be inscribed
– Inradius or Apothem r – a line segment from the center to the midpoint of one of its sides.

Using the formula below, the calculator will give you a result of an area of your polygon.

A = \frac{1}{4}\cdot n\cdot a^{2}\cdot cot(\frac{\pi }{n})

To find Apothem of a polygon, you can use this formula:

r = R\cdot cos(\frac{\pi }{n})

To find the Circumradius of a polygon, you can use the formula below:

R = r\cdot sec(\frac{\pi }{n})

 Features of the polygons

Check some more essential features of the polygon below:

– Two sides of a polygon are adjacent if they have a common vertex.
– Two adjacent sides determine the inner angle of a polygon.
– A polygon has an equal number of vertices, angles, and sides.
– A line whose endpoints are non-adjacent vertices of a polygon is called a diagonal of a polygon.
– The number of corners or pages determines the name of the polygon, so we have a triangle, quadrilateral, pentagon, hexagon…

 An example of using the area of a regular polygon calculator

Suppose that you want to calculate the area of a specific regular polygon. For example, a 6-sided polygon, called hexagon, with 2cm sides.

Firstly, enter the number of sides of the chosen polygon. Put number 6 into the number of sides box. Type in the polygon side length. In our example, it is equal to 2cm.

Our area of polygon calculator displays the measurement. It is equal to 10.39 cm².

Check our hexagon calculator to find more useful formulas with hexagons.

FAQ?

1. What must a polygon have?

 Every polygon is a two-dimensional shape and must have three or more points connected by line segments.

2. Is a circle considered a polygon?

A circle is not classified as a polygon. It is made up of curves and is defined as a closed two-dimensional figure.

3. How many vertices are there in the hendecagon?

A hendecagon is an eleven-sided polygon. So, we have eleven vertices in the hendecagon.

4. What is the total sum of all the interior angles of a regular decagon?

 If we want to find the total sum of all the interior angles of a regular decagon, we need to use the formula (n-2)(180). For example, finding the total sum of all the interior angles in a hendecagon would be equal to (11-2) x 180 = 9×180 = 1620.

5. Is an arch a polygon?

 An arch is half of a regular polygon.