1. **State the problem:** Calculate the volume of a prism with a trapezoidal base. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Area of base} \times \text{length}$$ 3. **Formula for area of trapezoid base:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides and $h$ is the height. 4. **Identify given values:** - $b_1 = 16$ cm (bottom width) - $b_2 = 8$ cm (top width) - $h = 7$ cm (height of trapezoid) - Length of prism $= 20$ cm 5. **Calculate area of trapezoid base:** $$\text{Area} = \frac{(16 + 8)}{2} \times 7 = \frac{24}{2} \times 7 = 12 \times 7 = 84 \text{ cm}^2$$ 6. **Calculate volume of prism:** $$\text{Volume} = 84 \times 20 = 1680 \text{ cm}^3$$ **Final answer:** The volume of the prism is $1680$ cubic centimeters.