To solve the problem, we need to find the value of $h$ in the given quadrilateral diagram. Here's the step-by-step explanation:

Diagram Analysis

1. The diagram shows a parallelogram-like shape with the following measurements:
   • The bottom side is labeled $15 \, \text{cm}$.
   • A diagonal divides the parallelogram into two right triangles.
   • In the triangle of interest, one leg is labeled $6 \, \text{cm}$, the other leg is $h \, \text{cm}$, and the diagonal is labeled $4 \, \text{cm}$.

This forms a right triangle where:

• $6 \, \text{cm}$ is one leg.
• $h \, \text{cm}$ is the other leg.
• $4 \, \text{cm}$ is the hypotenuse.

Applying the Pythagorean Theorem

For a right triangle, the Pythagorean theorem states: $a^2 + b^2 = c^2$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse. Substituting the values: $6^2 + h^2 = 4^2$

Simplify the Equation

1. Calculate the squares: $36 + h^2 = 16$
2. Solve for $h^2$: $h^2 = 16 - 36$ $h^2 = -20$

Conclusion

Here, the equation results in $h^2 = -20$, which is not possible for real numbers. This suggests there may be an error in the problem setup, such as incorrect labeling of the hypotenuse or sides, as a right triangle cannot have a hypotenuse shorter than either of its legs.

Suggestions

Double-check the dimensions or clarify the setup, as the provided triangle dimensions lead to an invalid scenario. Let me know if you want assistance verifying or exploring alternate interpretations of the problem.

Would you like to go over this further, or explore possible corrections?