Theory:

We know that a quadrilateral is made up of four sides. Any quadrilateral can be divided into two triangles with the help of a diagonal. This process of dividing a quadrilateral into triangles is called triangulation.
 
Let us look at the figure given below to know how a quadrilateral would look like after triangulation.
 
1.PNG
 
Here, \(\triangle ABD\) and \(\triangle BCD\) are formed after triangulation.
 
To find the area of the quadrilateral, we should know the values of \(h_1\) and \(h_2\). \(h_1\) and \(h_2\) are the perpendiculars drawn from the diagonal to the vertices. Let us look at the figure given below for a better understanding.
 
2.PNG
 
From the figure given above, we can come to the following inferences.
 
\(ABCD\) is a quadrilateral with \(d\) as the diagonal and \(h_1\) and \(h_2\) as its heights.
  
\(\text{Area of quadrilateral}\) \(ABCD =\) \((\text{Area of} \triangle ABD)\) \(+\) \((\text{Area of} \triangle BCD)\)
 
[Since the diagonal is divided into two triangles after triangulation]
 
\(=\) \((\frac{1}{2} \times BD \times h_1)\) \(+\) \((\frac{1}{2} \times BD \times h_2)\)
 
[Since,\(\text{Area of a triangle}= \frac{1}{2} \times b \times h\),where \(b\) and \(h\) are its base and height respectively]
 
\(=\) \(\frac{1}{2} \times BD \times (h_1 + h_2)\)
 
\(=\) \(\frac{1}{2} \times d \times (h_1 + h_2)\)
 
Therefore, \(\text{Area of a quadrilateral}\) \(=\) \(\frac{1}{2}d(h1 + h2)\) square units.