1. **State the problem:** We have a triangular prism with a triangular base having sides 6 in, 8 in, and 10 in, and the prism height (length) is 12 in. We need to find the volume and surface area of the prism. 2. **Volume formula:** The volume of a prism is given by $$V = B \times h$$ where $B$ is the area of the base and $h$ is the height (length) of the prism. 3. **Surface area formula:** The surface area of a prism is $$SA = 2B + Ph$$ where $B$ is the base area, $P$ is the perimeter of the base, and $h$ is the height of the prism. 4. **Find the base area $B$:** The base is a triangle with sides 6, 8, and 10 inches. Since $6^2 + 8^2 = 36 + 64 = 100 = 10^2$, the triangle is right-angled with legs 6 and 8 and hypotenuse 10. 5. Area of right triangle base: $$B = \frac{1}{2} \times 6 \times 8 = 24$$ square inches. 6. **Calculate volume:** $$V = B \times h = 24 \times 12 = 288$$ cubic inches. 7. **Calculate perimeter $P$ of base:** $$P = 6 + 8 + 10 = 24$$ inches. 8. **Calculate surface area:** $$SA = 2B + Ph = 2 \times 24 + 24 \times 12 = 48 + 288 = 336$$ square inches. **Final answers:** - Volume = 288 cubic inches - Surface area = 336 square inches