1. **State the problem:** We are given a trapezoid with bases of lengths 8 inches and 4 inches, an area of 30 square inches, 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:** $$30 = \frac{(8 + 4)}{2} \times h$$ 4. **Simplify the expression inside the fraction:** $$30 = \frac{12}{2} \times h$$ 5. **Simplify the fraction:** $$30 = 6 \times h$$ 6. **Solve for $h$ by dividing both sides by 6:** $$30 = 6 \times h$$ $$\Rightarrow \cancel{6} \times h = \frac{30}{\cancel{6}}$$ $$h = 5$$ 7. **Answer:** The height $h$ of the trapezoid is 5 inches.