1. **State the problem:** We need to find the area of a trapezoid with parallel sides of lengths 4 cm and 7 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:** $$\text{Area} = \frac{(4 + 7)}{2} \times 4$$ 4. **Simplify inside the parentheses:** $$\text{Area} = \frac{11}{2} \times 4$$ 5. **Multiply:** $$\text{Area} = \frac{11}{\cancel{2}} \times \cancel{2} \times 4 = 11 \times 2 = 22$$ 6. **Final answer:** The area of the trapezoid is $22$ square centimeters.