To calculate the surface area of the triangular prism, we need to calculate the areas of all the faces of the prism, which include the triangular bases and the three rectangular faces.

Step-by-Step Breakdown:

1. Calculate the area of the triangular bases:

   • The triangle is a right triangle with legs of 20 m and 48 m (from the diagram).
   • The area $A_{\text{triangle}}$ of a right triangle is given by: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$ So, $A_{\text{triangle}} = \frac{1}{2} \times 48 \times 20 = 480 \, \text{m}^2$
   • Since there are two triangular bases, the total area for both triangles is: $2 \times 480 = 960 \, \text{m}^2$

2. Calculate the areas of the three rectangular faces: The three rectangles are formed by the lengths of the triangle's sides and the length of the prism (52 m).

   • Rectangle 1 (side: 48 m, length of the prism: 52 m): $A_1 = 48 \times 52 = 2496 \, \text{m}^2$

   • Rectangle 2 (side: 20 m, length of the prism: 52 m): $A_2 = 20 \times 52 = 1040 \, \text{m}^2$

   • Rectangle 3 (side: 60 m, length of the prism: 52 m): $A_3 = 60 \times 52 = 3120 \, \text{m}^2$

3. Total Surface Area: Now, add the areas of the two triangular bases and the three rectangular faces: $\text{Total Surface Area} = 960 + 2496 + 1040 + 3120 = 7616 \, \text{m}^2$

Final Answer:

The surface area of the triangular prism is 7616 m².

Let me know if you need further details or have any questions.

Here are some follow-up questions to expand on this:

1. How would you calculate the volume of this triangular prism?
2. If the height of the prism changes, how would that affect the surface area?
3. Can you use the same method to calculate the surface area of a rectangular prism?
4. How would the surface area change if the dimensions of the triangular base were doubled?
5. What is the formula for the surface area of a triangular prism in general terms?

Tip: For prisms, surface area involves summing the areas of all faces, while volume uses the area of the base times the height (or length).