1. The problem states that the lateral surface area and the cross-sectional area of a prism are both 175 cm². 2. The lateral surface area (LSA) of a prism is the perimeter of the base times the height: $$LSA = P \times h$$. 3. The cross-sectional area (CSA) is the area of the base: $$CSA = A$$. 4. Given $$LSA = 175$$ and $$CSA = 175$$, we have: $$P \times h = 175$$ $$A = 175$$ 5. Without additional information (such as the shape of the base or the height), we cannot find unique values for perimeter, height, or base dimensions. 6. If you provide the shape of the base or the height, we can proceed to find the missing dimensions.