Theory:

A polygon is any shape with a minimum of three sides.
 
Let us consider the following pentagon \(ABCDE\) and try to find its area.
 
4.PNG
 
Area of a pentagon can be found in two ways.
Type \(1\)
Let us use the method of triangulation using two diagonals.
 
Let us look at the figure given below for a better understanding.
 
5.PNG
 
\(\text{Area of a pentagon} = \text{Area of}\) \(\triangle AED + \text{Area of}\) \(\triangle ABD + \text{Area of}\) \(\triangle BCD\)
Type \(2\)
Another way of obtaining the area of a pentagon is by drawing one diagonal and drawing two perpendiculars to that diagonal.
 
Let us look at the figure given below for a better understanding.
 
6.PNG
 
In the figure given above, \(BD\) is the diagonal, \(EO\) and \(AN\) are the two perpendiculars to \(BD\).
 
Here, \(\text{Area of a pentagon} = \text{Area of}\) \(\triangle ODE + \text{Area of}\) \(\triangle BCD + \text{Area of trapezium}\) \( AEON + \text{Area of}\) \(\triangle ABN\)