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Area of a polygon calculator

Area of a polygon calculator finds the primerer 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.

Calculate the area, perimeter of Polygon (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

    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 polygon.

     

    Regular polygon area calculator also includes 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

    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