To solve the problem, let us calculate the area of the rhombus using the given information.

Step-by-Step Solution:

1. Identify the formula for the area of a rhombus: The area of a rhombus is calculated as: $\text{Area} = \frac{1}{2} \cdot \text{Diagonal}_1 \cdot \text{Diagonal}_2$ Here, $WY$ is one diagonal, and $XZ$ is the other diagonal.

2. Determine the diagonal $XZ$: From the diagram:

   • $XW = x + 6$
   • $WZ = x + 9$

   Since $WZ$ and $XW$ meet at the center (and form right triangles), $XZ = XW + WZ$.

   Substitute $XW$ and $WZ$: $XZ = (x + 6) + (x + 9) = 2x + 15$

3. Solve for $x$: To find $x$, additional information is required (e.g., lengths or relationships), which does not seem fully specified in the image. However, if any further relationships between diagonals or properties are given, we could calculate the exact value.

4. Plug in the diagonals to compute the area: Assuming $x$ is provided or calculable, substitute: $\text{Area} = \frac{1}{2} \cdot WY \cdot XZ = \frac{1}{2} \cdot 30 \cdot (2x + 15)$

   Expand: $\text{Area} = 15 \cdot (2x + 15) = 30x + 225$

   At this stage, the specific value of $x$ is needed to get the exact numerical area.

Next Steps:

If the problem provides more context (like the exact value of $x$ or relationships for the rhombus), we can substitute and complete the solution. Let me know if you have more details to clarify further.

Questions:

1. What is the formula for the area of a rhombus in terms of diagonals?
2. Can the rhombus's properties (equal sides, perpendicular diagonals) help simplify calculations?
3. How do diagonals split the rhombus into four right triangles?
4. What additional information is needed to fully determine $x$?
5. Could trigonometric properties of the triangles be used here?

Tip:

Remember that in a rhombus, diagonals always bisect each other at right angles, which can simplify calculations!