1. **State the problem:** We are given a prism with a cross-sectional perimeter of 48 cm and a length of 10 cm. We need to find the lateral surface area of the prism. 2. **Recall the formula:** The lateral surface area (LSA) of a prism is given by the product of the perimeter of its cross section and its length: $$ \text{LSA} = \text{Perimeter} \times \text{Length} $$ 3. **Substitute the given values:** $$ \text{LSA} = 48 \times 10 $$ 4. **Calculate:** $$ \text{LSA} = 480 $$ 5. **Conclusion:** The lateral surface area of the prism is 480 square centimeters.