1. **Stating the problem:** Calculate the total surface area of a triangular prism with two right triangular faces and three rectangular faces. 2. **Given data:** - Triangular faces: base $b=10$ cm, height $h=24$ cm - Rectangular faces areas: $312$ cm², $120$ cm², and $288$ cm² 3. **Formula for the area of a right triangle:** $$\text{Area} = \frac{1}{2} \times b \times h$$ 4. **Calculate the area of one triangular face:** $$\frac{1}{2} \times 10 \times 24 = 120 \text{ cm}^2$$ 5. **Since there are two identical triangular faces, total triangular area:** $$2 \times 120 = 240 \text{ cm}^2$$ 6. **Sum of rectangular faces areas:** $$312 + 120 + 288 = 720 \text{ cm}^2$$ 7. **Total surface area $S$ is the sum of all faces:** $$S = 240 + 720 = 960 \text{ cm}^2$$ **Final answer:** The total surface area of the triangular prism is $960$ cm².