# Polygon Tutorial

## Polygon Tutorial

##### Polygon Definition:

A polygon is a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments.

#### Polygon Formula :

###### Using length of a side :
Area of Polygon = ((side)² * N) / (4Tan(π / N)) Perimeter of Polygon = N * (side)
Area of Polygon = ½ * R² * Sin(2π / N)
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
##### Polygon Image/Diagram ##### Case 1:

Find the area and perimeter of a polygon with the length 2 and the number of sides is 4.

###### Step 1:

Find the area.

 Area = ((side)² * N) / (4Tan(π / N)) = ((2)² * 4) / (4 * Tan(3.14 / 4)) = (4 * 4) / 4 * Tan(0.785) = 16 / 4 * 0.999 = 16 / 3.996 Area = 4.
###### Step 2:

Find the perimeter. Perimeter = (N * (side) = 4 * 2 = 8

##### Case 2:

Find the area of a polygon with the given radius 2 and the number of sides is 5.

###### Step 1:

Find the area.

 Area = ½ * R² * Sin(2π / N) = (0.5) * 2² * Sin(2 * 3.14 / 5) = 0.5 * 4 * Sin(6.28 / 5) = 2 * Sin(1.26) = 2 * 0.95 Area = 1.9.
##### Case 3:

Find the area of a polygon with the given radius 2 and the number of sides is 5 using Apothem.

###### Step 1:

Find the apothem.

 Apothem = R * Cos(π / N) = 2 * Cos(3.14 / 5) = 2 * Cos(0.63) = 2 * 0.81 Apothem = 1.62.
###### Step 2:

Find the area.

 Area = A² * N * Tan(π / N) = 1.62² * 5 * Tan(3.14 / 5) = 2.62 * 5 * Tan(0.63) = 13.1 * 0.73 Area = 9.5.
##### Case 4:

Find the area of a polygon with the length 2 and the number of sides is 4 using Apothem.

###### Step 1:

Find the apothem.

 Apothem = side / (2 * Tan(π / N)) = 2 / (2 * Tan(π / 4)) = 2 / (2 * Tan(0.785)) = 2 / (2 * 0.999) = 2 / 1.998 Apothem = 1.
###### Step 2:

Find the perimeter. Perimeter = (N * (side) = 4 * 2 = 8

###### Step 3:

Find the area.

 Area = (A * P) / 2 = (1 * 8) / 2 = 8 / 2 Area = 4.

The above example will clearly illustrates how to calculate the Area, Perimeter of a Polygon manually.

#### Related Calculator:

This tutorial will help you dynamically to find the Math area problems.