1. **State the problem:** Solve for $b$ in the formula $$A = h \left( \frac{a + b}{2} \right)$$ given $A = 10$, $h = 4$, and $a = 3$. 2. **Write the formula:** The area $A$ of a trapezoid is given by $$A = h \left( \frac{a + b}{2} \right)$$ where $a$ and $b$ are the lengths of the two parallel sides and $h$ is the height. 3. **Substitute the known values:** $$10 = 4 \left( \frac{3 + b}{2} \right)$$ 4. **Simplify the right side:** $$10 = \frac{4}{2} (3 + b)$$ $$10 = 2 (3 + b)$$ 5. **Divide both sides by 2 to isolate $(3 + b)$:** $$\frac{10}{\cancel{2}} = \cancel{2} (3 + b) / \cancel{2}$$ $$5 = 3 + b$$ 6. **Solve for $b$ by subtracting 3 from both sides:** $$5 - 3 = b$$ $$b = 2$$ **Final answer:** $$\boxed{b = 2}$$