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Polygon Calculator
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Polygon Calculator is used to find the perimeter of polygon, area of polygon( length of the side, apothem and length of the side).

There are different ways to calculate the area of polygon, below you can see formulas and some examples.

Regular Polygon
It is applicable for regular polygon.
 

Step by Step Calculation

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Step 1 :  

Formulas:


 


Area of Polygon (using length of a side) :




Area of Polygon = ((l)2 * N) / (4Tan($\pi$ / N))




Perimeter of Polygon = N * l




Where

N = number of sides

l = length of side


Area of Polygon (using apothem and length of a side):


Area of Polygon = $\frac{(A\ *\ P)}{2}$


where A = l / (2 * Tan ($\pi$ / N))



Step 2 :  

Put the values in the formula and calculate it further.



Example Problems

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  1. Find the area, apothem and perimeter of a polygon, whose length is 6 cm and number of sides is 5.


    Step 1 :  

    Given:




    Length of side ' l ' = 6 cm

    Number of sides ' N ' = 5


     


    Formulas:


     


    Area of Polygon (using length of a side) :




    Area of Polygon = ((l)2 * N) / (4Tan($\pi$ / N))




    Perimeter of Polygon = N * l


     


    Area of Polygon (using apothem and length of a side):


     



    Area of Polygon = $\frac{(A\ *\ P)}{2}$



    Step 2 :  

    Put the values in the formula and calculate it further.


     


    Area of Polygon (using length of a side) :


     


    Area of Polygon = ((6)2 * 5) / 4 * Tan($\pi$ / 5)




    Are of Polygon = 180 / 4 * Tan(3.142/ 5)


     


                          = 62 cm2


     


    Perimeter of Polygon = 5 * 6 = 30 cm


     


    Area of Polygon (using apothem and length of a side):


     


    We need to find first Apothem

    A = 6 / ( 2 * Tan($\pi$ / 5))

    A = 6 / (2 * Tan (0.628))

    A = 6 / (2 * 0.727)

    A = 4.126 cm



    Put ' A ' Values in the formula and caluclate it further



    Area of Polygon = (4.126 * 30)/2


    Area of Polygon = 62 cm2



    Answer  :  

    Area of Polygon (using length of a side) = 62 cm2

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Perimeter of Polygon = 30 cm

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Area of Polygon (using apothem and length of a side): 62 cm2



  2. Find the area, apothem and perimeter of a polygon, whose length is 4 cm and number of sides is 6.


    Step 1 :  

    Given:



    Length of side ' l ' = 4 cm

    Number of sides ' N ' = 6


    Formulas:


    Area of Polygon (using length of a side) :


    Area of Polygon = ((l)2 * N) / (4Tan($\pi$ / N))


    Perimeter of Polygon = N * l


    Area of Polygon (using apothem and length of a side):


    Area of Polygon = $\frac{(A\ *\ P)}{2}$



    Step 2 :  

    Put the values in the formula and calculate it further.


    Area of Polygon (using length of a side) :


    Area of Polygon = ((4)2 * 6) / 4 * Tan($\pi$ / 6)


    Are of Polygon = 96 / 4 * Tan(3.142/ 6)




    Area of polygon = 96 / 4 * 0.578




    Area of polygon = 96 / 2.312


                          = 41.52 cm2

     

    Perimeter of Polygon = 4 * 6 = 24 cm


    Area of Polygon (using apothem and length of a side):


    We need to find first Apothem


    A = 4 / ( 2 * Tan( 3.142 / 6))

    A = 4 / (2 * 0.578)

    A = 4 / 1.156

    A = 3.460 cm


    Put ' A ' Values in the formula and caluclate it further


    Area of Polygon = (3.460 * 24)/2


    Area of Polygon = 41.52 cm2



    Answer  :  

    Area of Polygon (using length of a side) = 41.52 cm2

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Perimeter of Polygon = 24 cm

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Area of Polygon (using apothem and length of a side): 41.52 cm2



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