To find the surface area of the triangular prism, we can use the net provided in the diagram. The surface area consists of:

1. Two triangular faces.
2. Three rectangular faces.

1. Area of the triangular faces:

The triangle is a right triangle with a base of 5 m and a height of 12 m.

$\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $= \frac{1}{2} \times 5 \times 12 = 30 \, \text{m}^2$ Since there are two identical triangular faces: $\text{Area of two triangles} = 2 \times 30 = 60 \, \text{m}^2$

2. Area of the rectangular faces:

• One rectangle has a length of 13 m (the hypotenuse of the triangle) and a width of 16 m.

$\text{Area of this rectangle} = 13 \times 16 = 208 \, \text{m}^2$

• Another rectangle has a length of 12 m (the height of the triangle) and a width of 16 m.

$\text{Area of this rectangle} = 12 \times 16 = 192 \, \text{m}^2$

• The final rectangle has a length of 5 m (the base of the triangle) and a width of 16 m.

$\text{Area of this rectangle} = 5 \times 16 = 80 \, \text{m}^2$

3. Total Surface Area:

Now, add up all the areas: $\text{Total Surface Area} = 60 + 208 + 192 + 80 = 540 \, \text{m}^2$

Thus, the surface area of the triangular prism is 540 square meters.

Do you want further details or have any questions? Here are some related questions:

1. How is the hypotenuse of the right triangle calculated in a triangular prism?
2. Can you calculate the volume of the triangular prism based on the given dimensions?
3. How do you find the surface area of more complex solids like pyramids or cylinders?
4. What is the significance of using nets to solve surface area problems?
5. What are some real-life applications of calculating surface area in construction or design?

Tip: Always break down composite shapes into simpler parts like triangles and rectangles when solving for surface area or volume.