1. **Problem Statement:** Find the missing height $H$ of a right triangular prism with volume $432$ cm³ and base sides $12$ cm and $8$ cm. 2. **Formula:** Volume of a prism is given by $$V = \text{Base Area} \times H$$ 3. **Calculate Base Area:** For a right triangle base, $$\text{Base Area} = \frac{1}{2} \times 12 \times 8 = 48 \text{ cm}^2$$ 4. **Find Height $H$:** Using $$H = \frac{V}{\text{Base Area}} = \frac{432}{48}$$ 5. **Simplify:** $$H = \frac{432}{48} = 9 \text{ cm}$$ 6. **Explanation:** The height of the prism is $9$ cm because the volume divided by the base area gives the height. --- 1. **Problem Statement:** Find the missing base area of a rectangular prism with volume $420$ cm³ and height $7$ cm. 2. **Formula:** $$V = \text{Base Area} \times H$$ 3. **Find Base Area:** $$\text{Base Area} = \frac{V}{H} = \frac{420}{7}$$ 4. **Simplify:** $$\text{Base Area} = 60 \text{ cm}^2$$ 5. **Explanation:** The base area is $60$ cm² because dividing the volume by the height gives the base area. --- **Final answers:** - Height of triangular prism: $9$ cm - Base area of rectangular prism: $60$ cm²