Regular Polygon Calculator

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.
Calculate the area, perimeter of Polygon (Polygon Calculator)
Length :
Number of Sides :
Area of Polygon [Using length of a side]:
Area of Polygon [Using apothem and length of a side]:
Perimeter of Polygon:
 
Radius :
Number of Sides :
Area of Polygon [Using radius (circumradius)]:
Area of Polygon [Using apothem (inradius)]:
 
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

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 polygon.

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

Step 2: Find the perimeter.
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.

Step 1: Find the area.
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.

Step 1: Find the apothem.
Apothem = R * Cos (π / N)
= 3 * Cos (3.14 / 5)
= 3* Cos (0.63)
= 3 * 0.808
Apothem = 2.43

Step 2: Find the area.
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.

Step 1: Find the apothem.
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

Step 2: Find the perimeter.
Perimeter = (N * (side) = 4 * 3= 12

Step 3: Find the area.
Area = (A * P) / 2
= (1.501 * 12) / 2
= 18.012 / 2
Area = 9.006