1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 2 cm and 4 cm, and a height of 6 cm. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{Base}_1 + \text{Base}_2)}{2} \times \text{Height}$$ 3. **Identify the values:** - Base 1 ($b_1$) = 2 cm - Base 2 ($b_2$) = 4 cm - Height ($h$) = 6 cm 4. **Substitute the values into the formula:** $$\text{Area} = \frac{(2 + 4)}{2} \times 6$$ 5. **Simplify inside the parentheses:** $$\text{Area} = \frac{6}{2} \times 6$$ 6. **Divide:** $$\text{Area} = 3 \times 6$$ 7. **Multiply:** $$\text{Area} = 18$$ 8. **Conclusion:** The area of the trapezoid is 18 square centimeters.