1. **State the problem:** We are given a trapezoid with bases of lengths 4 km and 8 km, an area of 42 square kilometers, and we need to find the height $h$. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times h$$ 3. **Substitute the known values:** $$42 = \frac{(4 + 8)}{2} \times h$$ 4. **Simplify the expression inside the fraction:** $$42 = \frac{12}{2} \times h$$ 5. **Simplify the fraction:** $$42 = 6 \times h$$ 6. **Solve for $h$ by dividing both sides by 6:** $$42 = \cancel{6} \times h \\ \frac{42}{\cancel{6}} = h$$ 7. **Calculate the division:** $$h = 7$$ **Final answer:** The height $h$ of the trapezoid is 7 kilometers.