To determine the missing length \( l \) of the triangular prism with a given surface area of 524 square centimeters, we need more information about the prism's dimensions, such as the base and height of the triangular face, or possibly the formula for the surface area if it is provided.
The surface area \( A \) of a triangular prism can be calculated using the formula:
\[ A = \text{Base Area} + \text{Lateral Area} \]
Where:
- Base Area = Area of the triangular base
- Lateral Area = Perimeter of the base triangle × height of the prism
Without specific measurements or the shape of the triangle, it is impossible to calculate the missing length with just the surface area provided.
If any additional information about the prism is available (like dimensions of the triangle), please provide it to proceed with the calculations. Based on the options you provided (10 cm, 17 cm, 8 cm, and 16 cm), we could find a solution if we know how these lengths relate to the dimensions of the prism.
Please clarify or provide more details regarding the dimensions of the triangular prism.