1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 38 cm and 18 cm, and legs of 16 cm (height) and 20 cm. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel bases, and $h$ is the height (the perpendicular distance between the bases). 3. **Identify the values:** - $b_1 = 38$ cm (top base) - $b_2 = 18$ cm (bottom base) - $h = 16$ cm (height given as the vertical leg) 4. **Calculate the area:** $$\text{Area} = \frac{(38 + 18)}{2} \times 16$$ 5. **Simplify inside the parentheses:** $$\text{Area} = \frac{56}{2} \times 16$$ 6. **Simplify the fraction:** $$\text{Area} = 28 \times 16$$ 7. **Multiply:** $$\text{Area} = 448$$ 8. **Conclusion:** The area of the trapezoid is **448 square centimeters**.