### 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.

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.

\(\text{Area of a pentagon} = \text{Area of}\) \(\triangle AED + \text{Area of}\) \(\triangle ABD + \text{Area of}\) \(\triangle BCD\)

Type \(2\)

Let us look at the figure given below for a better understanding.

In the figure given above, \(BD\) is the diagonal, \(EO\) and \(AN\) are the two perpendiculars to \(BD\).

Here, \(\text{Area of a pentagon} = \text{Area of}\) \(\triangle ODE + \text{Area of}\) \(\triangle BCD + \text{Area of trapezium}\) \( AEON + \text{Area of}\) \(\triangle ABN\)