To solve the surface area of the triangular prism using the given net, we will calculate the area of each of its components and then sum them up.

The net consists of:

1. Two identical triangles (the bases of the prism).
2. Three rectangles (the sides of the prism).

Step-by-step breakdown:

1. Area of the two triangles:

• The base of each triangle is 6 feet, and the height is 8 feet (from the diagram).
• The formula for the area of a triangle is: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area of one triangle} = \frac{1}{2} \times 6 \, \text{ft} \times 8 \, \text{ft} = 24 \, \text{ft}^2$ Since there are two triangles: $\text{Total area of triangles} = 2 \times 24 \, \text{ft}^2 = 48 \, \text{ft}^2$

2. Area of the three rectangles:

• First rectangle (15 ft by 10 ft): $\text{Area} = 15 \, \text{ft} \times 10 \, \text{ft} = 150 \, \text{ft}^2$
• Second rectangle (15 ft by 8 ft): $\text{Area} = 15 \, \text{ft} \times 8 \, \text{ft} = 120 \, \text{ft}^2$
• Third rectangle (15 ft by 8 ft): $\text{Area} = 15 \, \text{ft} \times 8 \, \text{ft} = 120 \, \text{ft}^2$

3. Total surface area:

Now, summing up the areas of the triangles and rectangles: $\text{Total surface area} = 48 \, \text{ft}^2 + 150 \, \text{ft}^2 + 120 \, \text{ft}^2 + 120 \, \text{ft}^2$ $\text{Total surface area} = 438 \, \text{ft}^2$

Thus, the total surface area of the triangular prism is 438 square feet.

Would you like more details or have any questions? Here are five follow-up questions that expand on this concept:

1. How would the surface area change if the height of the triangular base were increased?
2. How do you calculate the volume of the triangular prism using the same dimensions?
3. What are other real-world applications of surface area calculations for triangular prisms?
4. How does changing the length of the prism's side impact the surface area?
5. Can you derive the formula for the lateral surface area of a triangular prism?

Tip: Always break down complex shapes into simpler parts like triangles and rectangles when calculating surface areas.