1. **State the problem:** We are given a trapezoid with an area of 42 square kilometers. The trapezoid has bases of lengths 4 km and 8 km, and we need to find its 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:** $$42 = \frac{12}{2} \times h$$ $$42 = 6h$$ 5. **Solve for $h$:** $$h = \frac{42}{6} = 7$$ 6. **Answer:** The height $h$ of the trapezoid is 7 kilometers.