1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 8 cm and 12 cm, and a height of 4 cm. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{Base}_1 + \text{Base}_2)}{2} \times \text{Height}$$ 3. **Substitute the given values:** $$\text{Area} = \frac{(8 + 12)}{2} \times 4$$ 4. **Simplify inside the parentheses:** $$\text{Area} = \frac{20}{2} \times 4$$ 5. **Simplify the fraction:** $$\text{Area} = \cancel{\frac{20}{2}}^{10} \times 4$$ 6. **Multiply to find the area:** $$\text{Area} = 10 \times 4 = 40$$ 7. **Final answer:** The area of the trapezoid is **40 square centimeters**.