1. **State the problem:** We need to find the volume of a prism whose cross-section is a trapezoid with bases 12 cm and 4 cm, and height 4 cm. The length (depth) of the prism is 5 cm. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Area of cross-section} \times \text{length}$$ 3. **Formula for area of a trapezoid:** $$\text{Area} = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the two parallel sides, and $h$ is the height. 4. **Calculate the area of the trapezoid cross-section:** Given $a = 12$ cm, $b = 4$ cm, and $h = 4$ cm, $$\text{Area} = \frac{(12 + 4)}{2} \times 4 = \frac{16}{2} \times 4 = 8 \times 4 = 32 \text{ cm}^2$$ 5. **Calculate the volume of the prism:** Length $= 5$ cm, $$\text{Volume} = 32 \times 5 = 160 \text{ cm}^3$$ **Final answer:** $$\boxed{160 \text{ cm}^3}$$