Let's solve the problem.

The formula for the area of a trapezoid is:

$A = \frac{1}{2} h (y + z)$

We are tasked with solving for $h$ in terms of $A$, $y$, and $z$.

Step-by-Step Solution:

1. Start with the given equation: $A = \frac{1}{2} h (y + z)$

2. Eliminate the fraction by multiplying both sides by 2: $2A = h (y + z)$

3. Solve for $h$ by dividing both sides by $(y + z)$: $h = \frac{2A}{y + z}$

Thus, the correct answer is:

$\boxed{\text{C: } h = \frac{2A}{y + z}}$

Let me know if you need further clarification or have additional questions! Here are some related questions to expand understanding:

1. What happens if $y + z = 0$ in the formula $h = \frac{2A}{y + z}$?
2. How do you derive the formula for the area of a trapezoid from its geometry?
3. Can this formula be used for other polygons like triangles? Why or why not?
4. How does the formula change if the base lengths of the trapezoid are equal?
5. What are some real-world applications of finding the height of a trapezoid?

Tip: Always isolate the variable step by step, and simplify fractions to avoid errors!