### 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.

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.

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.