To calculate the area of the quadrilateral shown in the image, we can divide the shape into two triangles and calculate the area of each separately.

Step 1: Divide into two triangles

The quadrilateral is divided into:

1. Triangle $\triangle ABD$
2. Triangle $\triangle BCD$

For $\triangle ABD$:

We use the formula for the area of a triangle when two sides and the included angle are given: $\text{Area} = \frac{1}{2} \times AB \times AD \times \sin(\theta)$ Here $AB = 4.5$, $AD = 9.2$, and the angle can be calculated if coordinates or angles are provided. Alternatively, we can use Heron’s formula if the missing side $BD$ is known.

For $\triangle BCD$:

Similarly, the area of $\triangle BCD$ can be calculated if the side $BD$ is known. Or, Heron’s formula can be applied if all sides are available.

Do you know any additional details about angles or coordinates? If not, I can calculate this assuming perpendicularity or using general properties. Let me know your preference!