1. The problem is to solve the formula for the area of a trapezoid, given by $$A = \frac{1}{2} h (x + y)$$, for the height $h$. 2. The formula relates the area $A$, the height $h$, and the lengths of the two parallel sides $x$ and $y$. 3. To isolate $h$, start by multiplying both sides by 2 to eliminate the fraction: $$2A = \cancel{2} \times \frac{1}{\cancel{2}} h (x + y) = h (x + y)$$ 4. Now divide both sides by $(x + y)$ to solve for $h$: $$h = \frac{2A}{x + y}$$ 5. This is the formula for the height $h$ in terms of the area $A$ and the lengths of the parallel sides $x$ and $y$. 6. Important note: $x + y$ must not be zero to avoid division by zero. Final answer: $$\boxed{h = \frac{2A}{x + y}}$$