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# Area of a polygon calculator

Enter the length, radius, and number of sides in the input boxes, press the **calculate **button to find the area using the area of a polygon calculator

Table of Contents:

**Formula**

__Using length of a side :__

Area of Polygon = ((side)² * N) / (4Tan(π / N))

Perimeter of Polygon = N * (side)

__Using radius (circumradius) :__

Area of Polygon = ½ * R² * Sin(2π / N)

__Using apothem (inradius) :__

Area of Polygon = A² * N * Tan(π / N)

where A = R * Cos(π / N)

__Using apothem and length of a side :__

Area of Polygon = (A * P) / 2

where A = side / (2 * Tan (π / N))

**where,**

N = Number of sides, A = Apothem, R = Radius, P = Perimeter

Area of a polygon calculator finds the perimeter and area of a regular polygon. A Polygon is a closed plane figure having three or more sides. A Polygon is a closed plane figure bounded by three or more straight sides which are equal and also all interior angles are equal.

## Regular polygon area calculator

A number of coplanar line segments, each connected end to end to form a closed shape are known as a Polygon. Triangles, rectangles, and pentagons are examples of the polygon.

Regular polygon area calculator also includes the perimeter of a polygon calculator.

__Examples__:

Case 1: Find the area and perimeter of a polygon with the length 3 and the number of sides is 4.

** Step 1:** Find the area.

Area = ((side)² * N) / (4Tan(π / N))

= ((3)² * 4) / (4 * Tan(3.14 / 4))

= (9 * 4) / 4 * Tan(0.785)

= 36/ 4 * 0.999

= 36/ 3.996

**Area**=9.009

**Find the perimeter.**

__Step 2__:**Perimeter**= (N * (side) = 4 * 3 = 12

Case 2: Find the area of a polygon with the given radius 3 and the number of sides is 5.

**Find the area.**

__Step 1__:Area = ½ * R² * Sin(2π / N)

= (0.5) * 3² * Sin(2 * 3.14 / 5)

= 0.5 * 9 * Sin(6.28 / 5)

= 2 * Sin(1.26)

= 4.5 * 0.95

**Area**= 4.275

Case 3: Find the area of a polygon with the given radius 3 and the number of sides is 5 using Apothem.

**Find the apothem.**

__Step 1__:Apothem = R * Cos (π / N)

= 3 * Cos (3.14 / 5)

= 3* Cos (0.63)

= 3 * 0.808

**Apothem**= 2.43

**Find the area.**

__Step 2__:Area = A² * N * Tan(π / N)

= 2.43² * 5 * Tan(3.14 / 5)

= 5.90 * 5 * Tan(0.63)

= 29.52* 0.73

**Area**=21.552

Case 4: Find the area of a polygon with the length 3 and the number of sides is 4 using Apothem.

**Find the apothem.**

__Step 1__:Apothem = side / (2 * Tan(π / N))

= 3/ (2 * Tan(π / 4))

= 3 / (2 * Tan(0.785))

= 3/ (2 * 0.999)

= 3 / 1.998

**Apothem**= 1.501

**Find the perimeter.**

__Step 2__:**Perimeter**= (N * (side) = 4 * 3= 12

**Find the area.**

__Step 3__:Area = (A * P) / 2

= (1.501 * 12) / 2

= 18.012 / 2

**Area**= 9.006