Area of Regular Polygon Calculator

Enter the number of sides(n)=
Enter the side length(S)=
Area of the Polygon= square units

Area of Regular Polygon Calculator is a free online tool that displays the area occupied by the regular polygons in the two-dimensional plane. BYJU’S online area of regular polygon calculator tool performs the calculation faster and it displays the area of a regular polygon in a fraction of seconds.

How to Use the Area of Regular Polygon Calculator? 

The procedure to use the area of regular polygon calculator is as follows:

Step 1: Enter the number of sides and side length in the input field (Example: n=5, S= 3)

Step 2: Now click the button “Solve” to get the regular polygon area

Step 3: Finally, the area of the regular polygon will be displayed in the output field (I.e., Area of Regular Polygon, A= 15.485 square units)

What is Meant by the Area of Regular Polygon?

In Geometry, a polygon is a plane figure with the straight sides, A polygon should have at least three sides. There are different types of polygon, namely regular polygon, irregular polygon, convex polygon, concave polygon, and so on. A regular polygon should have equal side lengths and equal angle. It means that a polygon should be equiangular and equilateral. Whereas the irregular polygon has unequal side lengths and angles. The area of the regular polygon is the region occupied by the regular polygon. Based on the number of sides of a polygon, it is classified as a triangle, quadrilateral, pentagon, etc. The area of the regular polygon is given by

If “n” is the number of sides of a polygon, and “s” is the side length of the polygon, then

The Area of a regular polygon, A = [S2n]/[4tan(180/n)] Square units

If the circum-radius “r” of the regular polygon is given, then

A = [r2n sin(360/n)]/2 Square units

Area of Regular Polygon Example

Example 1

Calculate the area of the regular polygon given that the number of sides is 5 and the side length is 3cm 

Solution:

Given that, number of sides, n = 5

Side length, S = 3cm

We know that the area of the regular polygon = [S2n]/[4tan(180/n)] 

By substituting the values, we get

A = [32 (5)]/[4tan(180/5)] 

A = (45)/(4 tan 36)

A = 45/ 4(0.7265)

A = 45/2.906

A = 15.485

Therefore, the area of a regular pentagon = 15.485 cm2

Also, check: Area of Regular Polygon Formula

Example 2:

Evaluate the area of the regular pentagon whose circum-radius is 2cm.

Solution:

Given that, circumradius  = 2 cm

Number of sides = 5

If the circumradius is given, the area of the regular pentagon is given as:

Area = [r2n sin(360/n)]/2 Square units

A =[22(5) sin(360/5)]/2

A =[20 sin(360/5)]/2

A =[20 sin 72]/2

A = 20(0.951)/2

A = 19.02/2

A = 9.51

Therefore, the area of the regular pentagon with radius 2 cm is 9.51cm2.

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