Complex Polygon

Complex polygon is a polygon whose sides cross over eachother one or more times. If the number of cross over increases, the complexity of the polygon also increases. Below are some of the complex polygons

Area of a Complex Polygon


There are three steps to find the area of the complex polygon. They are as follows:

Step 1: Break the polygon into simple rectangle, square or triangle.

Step 2: Find the area of all rectangle, square or triangle.

Step 3: Add all the area and get the area of complex polygon.

With the help of the above steps, we can easily find the area of any complex polygons.


Examples

Given below are some of the examples to find the area of a complex polygon.

Example 1:

Find the area of following polygon


DE= 5cm, EF =8cm, FD = 5 cm, AB = 14cm, CD = 10cm and the distance between these two parallel side AB and CD is 5cm

Solution:

Step 1: Break the polygon into triangle and trapezoid.


Here, the given complex polygon is braked into two simple polygon. It is separated at the point D

Step 2: Find the area of triangle (D1EF) and trapezoid (ABCD2).

Area of triangle (D1EF)

Value of s = (D1E + EF + FD1) / 2

Value of s = (5+8+5) / 2

Value of s = 9 cm

Area of triangle (D1EF) = SquareRoot (s(s - D1E)(s - EF)(s - FD1))

= SquareRoot (9(9 - 5)(9 - 8)(9 - 5))

= SquareRoot (9 x 4 x1 x 4)

=  SquareRoot (144)

= 12 square cm

Area of Trapezoid (ABCD2) =  ½ ( AB +CD2 ) x ( Perpendicular distance between AB  and  CD2 )

= ½ (10 +14) x 5

= ½ (24) x 5

= 12 x 5

= 60 square cm

Step 3: Add all the area of triangle and trapezoid to get area of complex polygon.

Area of Complex polygon = Area of triangle (D1EF) + Area of Trapezoid ABCD2)

= 12 square cm  +  60 square cm

= 72 square cm