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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.

It is applicable for regular polygon.

## Step by Step Calculation

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

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

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

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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