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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.


Table of Contents:

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    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