1. **State the problem:** Find the lateral and total surface area of the rectangular prism with base dimensions 10.5 cm by 4 cm and height 8.25 cm. 2. **Formulas:** - Lateral surface area $S_{lat} = P \times h$, where $P$ is the perimeter of the base and $h$ is the height. - Total surface area $S_{total} = P(h + 2b)$, where $b$ is the base width. 3. **Calculate the perimeter of the base:** $$P = 2(10.5 + 4) = 2(14.5) = 29$$ 4. **Calculate the lateral surface area:** $$S_{lat} = P \times h = 29 \times 8.25 = 239.25$$ 5. **Calculate the total surface area:** $$S_{total} = P(h + 2b) = 29(8.25 + 2 \times 4) = 29(8.25 + 8) = 29(16.25) = 471.25$$ 6. **Final answer:** - Lateral surface area = $239.25$ cm² - Total surface area = $471.25$ cm²