# Area of Regular Polygon Calculator

**Area of a Regular Polygon Calculator: **Do you feel it is very tough to compute the area of a regular polygon? Then you have reached the correct place. The simple and easy method to find the area of a regular polygon is provided in the following sections. Students must learn these type of geometrical shapes when they are promoting to the higher classes. With the help of this online tool, you can make the calculations at a faster pace.

### Formula to Compute Regular Polygon Area

Polygon is a two dimensional plane with straight lines. The formula to find the area of a regular polygon is mentioned here

Area of a regular polygon a = n * s² * cot(π/n) / 4

Area = n * s * apothem / 2

Regular polygon area = p * apothem / 2

Where,

n is the number of sides of a polygon.

s is the length of side of a regular polygon.

p is the perimeter of a regular polygon.

apothem is apothem of a polygon.

### Simple Procedure to Find Regular Polygon Area

Never think that calculating the area of a regular polygon is very difficult. The simple steps offered below will help you in solving the polygon area questions. Follow these instructions and solve the problems carefully.

- Make a note of the two important parameters i.e length of side of a regular polygon, number of sides of a polygon.
- Compute the square of side length and multiply the result by polygon number of sides.
- Divide the obtained value by 4.
- Get cot(π/polygon sides number).
- Multiply it with the output obtained in 4th step to know the area.

### Examples of Regular Polygon Area

**Example 1: **Calculate the area of 5 sided polygon with a side length 7 cm?

**Solution: **

Given that,

Number of sides of a polygon n = 5

The length of side of polygon s = 7 cm

Area of regular polygon a = n * s² * cot(π/n) / 4

By substituting the given values,

area = 5 * 7² * cot(π/5) / 4

= 5 * 7 * 7 * cot(π/5) / 4

= 245 * cot(π/5) / 4

= 245 * 91.2317 / 4

= 22351.76 / 4

= 5587.94

∴ Area of a 5 sided polygon with side length 7 cm is 5587.94 cm².

**Example 2: **Find area of a 12 sided polygon? The perimeter of regular polygon is 60 cm?

**Solution: **

Given that,

Number of sides of a polygon n = 12

Perimeter of the regular polygon = 60 cm

Perimeter of 12 sided regular polygon formula is perimeter = 12 * side

60 = 12 * side

60 / 12 = side

side = 5

Area of regular polygon a = n * s² * cot(π/n) / 4

area = 12 * 5² * cot(π/5) / 4

= 12 * 5² * 91.231 / 4

= 12 * 5 * 5 * 91.231 / 4

= 27,369.3 / 4

= 6,842.32

∴ Area of a 12 sided polygon is 6,842.32 cm².

You can get the information regarding geometry concepts on our site Areavolumecalculator.com

### FAQs on Regular Polygon Area Calculator

**1. What is meant by regular polygon?**

Regular polygon means a closed two dimensional plane having straight lines of equal length and all the interior angles are of equal size. The number of sides in the geometrical figure can be any real number. All the vertices of a regular polygon lie on a common circle.

**2. Find the area of of 9 sided regular polygon? Apothem and side length of polygon is 7 inches and 5 inches.**

Apothem = 7 inches, side length = 5 inches

number of sides = 9

Perimeter of polygon = 9 * 5 = 45 inches

Area of polygon = 1/2 (apothem) * (perimeter)

= 1/2 (7) * (45)

= 315 / 2

Area = 157.5 inches².

**3. How do you find the area of a regular polygon using calculator?**

Students must have to provide the number of sides of polygon and side length in the allotted input sections and hit on the calculate button to display the output easily.

**4. How do you find the regular polygon area with only the side length?**

The formula to check the regular polygon area by using the length of side is as follows:

Area = n * s² * cot(π/n) / 4 or (n * s²) / (4 * tan(π/n))

Where n is the number of sides, s is the side length.