1. **State the problem:** Calculate the volume of a composite prism with two sections: a taller section of height 10 cm and a shorter section of height 4 cm. 2. **Identify dimensions:** - Height of taller section: $10$ cm - Height of shorter section: $4$ cm - Length of base beneath shorter section: $5$ cm - Width of prism: $8$ cm - Total length of prism's side: $12$ cm 3. **Understand the shape:** The prism consists of two rectangular sections side by side along the length: one with length $5$ cm (shorter section) and the other with length $12 - 5 = 7$ cm (taller section). 4. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Height}$$ Since the prism is rectangular, volume is length $\times$ width $\times$ height. 5. **Calculate volume of shorter section:** $$V_1 = 5 \times 8 \times 4 = 160 \text{ cm}^3$$ 6. **Calculate volume of taller section:** $$V_2 = 7 \times 8 \times 10 = 560 \text{ cm}^3$$ 7. **Calculate total volume:** $$V = V_1 + V_2 = 160 + 560 = 720 \text{ cm}^3$$ **Final answer:** The volume of the prism is $720$ cubic centimeters.