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Area of Polygon: Formula, Methods, Calculator, Derivation with Examples

Area of Polygon

In mathematics a figure bounded by a finite number of sides is referred as Polygon. There are several Formula, Methods, Calculator, and Derivation to find out the Area of Polygon. Polygon is not a particular shape it can be a square, rectangle, trapezium, pentagon etc.

If you are looking for Area Of Polygon Formula along with examples then you may go through this page of as here we have provided the concept of Area Of A Polygon along with formulas and examples. Please take a look…

Area Of Polygon

Types of Polygon:

There are two types of Polygon:

  1. Regular Polygon
  2. Irregular Polygon

Area of Polygon

Regular Polygon

Now the question is – What is a Regular Polygon or how to find out the Area Of Regular Polygon?

In mathematics a regular polygon is a figure whose all the sides are equal in measurement. Regular polygons may be convex or star.

How To Calculate Area With Examples: Area Of Parallelogram

Area Of A Regular Polygon

Area Of Regular Polygon With N Sides

The formula for calculating the area of a regular polygon with length of the apothem (A) and perimeter (P) is,

Area Of Regular Polygon Formula = 1/2 AP or 1/2 perimeter * apothem

The formula for calculating the area of a regular polygon with ‘N’ sides and side length ‘S’ is,

Area Of A Polygon With N Sides= (S2N)/(4tan(π/N))

The formula for calculating the area of the regular polygon with inradius A and N sides is,

Area Of A Polygon Of N Sides= A2N tan(π/N)

The formula for calculating the area of the regular polygon with circumradius R and N number of sides is,

Area of a Polygon = R2N/2 sin (2πN)

Inradius – Distance from the center of any polygon to the sides of the polygon.

Circumradius – Distance from the center of the polygon to any of the vertices.

Know Here: How to Find the Area of a Sector?

Area Of Polygon With 4 Sides

Area Of Polygon With 4 Sides

Sr. No.4 sided PolygonsArea Formulas
1Squareside * side
2.Rectanglelength * width
3.ParallelogarmBase * height
4.Trapezoidh/2 (Sum of parallel sides)
5.Kite12 * longest diagonal * smallest diagonal

Example of Area of a regular Polygon:

Calculate the area of the polygon with an inradius of 6 cm and 7 sides.


Given: N = 7 and A = 6 cm

The formula for the area of the regular polygon with inradius A and N sides is,

Area = A2 N tan (π/N)

= (7)(6)2×tan(π/7)

= 7 * 36 * 0.481

= 121.2 

Hence, the area of the given polygon is 121.2 cm2.

Also Get Here: Area of Hexagon Formula

Area Of Irregular Polygon

Irregular polygons are polygons that do not have equal sides or equal angles.

There is no particular formula to find out the Area Of an Irregular Polygon. To Calculate Area Of Irregular Polygon firstly you need to divide the figure into triangles and square/rectangle (according to the figure)

Afterwards add the area of both and the final answer will be the Area Of An Irregular Polygon

Let’s understand the concept of Area Of Irregular Polygon Formula with an example:

For example, 

The figure shown below is the combination of rectangle and square.

And so, to find its area, we have to find the areas of the square and rectangle that are seen inside the irregular polygon and then add up.

Given below are some of the examples:

Example 1: Find the area of this figure.


In the figure, one of the shape is square and other one is a triangle.
Lets divide the figure by drawing a straight dotted line.

First, find the area of triangle and square and then, add the area of both the figures.

Step 1: Area of the triangle

Formula: Area of the triangle = 1212 (base * height)

Here, Base = 12, and

Height = 8

Area = 1212 * 12 * 8

= 48 sq units

Step 2: Area of the square

Formula:  Area of square = Side * Side

Side = 12

Area = 12 * 12

= 144  sq units

Step 3:

Total area = Area of triangle + Area of square

= 48 + 144

= 192 sq units.

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

To find out the Area Of Any Polygon you can use the formula given here on this page easily. We hope after going through this page you will not get confused about How To Calculate Area Of Polygon.

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