The image you've uploaded shows the net of a right triangular prism, and you need to calculate its surface area. Here's how to break down the steps:

1. Understanding the components: The net includes:

   • Two triangular faces (the ends of the prism).
   • Three rectangular faces (the sides of the prism).

2. Dimensions given:

   • The triangle has a base of 8 m and a height of 3 m.
   • The side rectangles have dimensions:
     • Two of them are 8 m × 6 m.
     • One of them is 7.4 m × 6 m.

3. Calculating the areas:

   • Area of each triangular face: The area of a triangle is given by $A = \frac{1}{2} \times \text{base} \times \text{height}$. $A = \frac{1}{2} \times 8 \, \text{m} \times 3 \, \text{m} = 12 \, \text{m}^2$ Since there are two triangular faces: $\text{Total area of triangles} = 2 \times 12 = 24 \, \text{m}^2$

   • Area of the three rectangular faces:

     • The two rectangles with dimensions 8 m × 6 m have areas: $A = 8 \, \text{m} \times 6 \, \text{m} = 48 \, \text{m}^2 \, \text{(each rectangle)}.$ So, for both of them: $48 \, \text{m}^2 + 48 \, \text{m}^2 = 96 \, \text{m}^2$
     • The remaining rectangle with dimensions 7.4 m × 6 m has an area: $A = 7.4 \, \text{m} \times 6 \, \text{m} = 44.4 \, \text{m}^2$

4. Total surface area: Adding up all the areas: $\text{Total area} = 24 \, \text{m}^2 \, (\text{triangular faces}) + 96 \, \text{m}^2 + 44.4 \, \text{m}^2 = 164.4 \, \text{m}^2$

Thus, the total surface area of the net of the right triangular prism is 164.4 m².

Would you like to explore more details, or do you have any further questions on this calculation?

Here are 5 related questions:

1. How would the surface area change if the height of the triangle was increased?
2. What would happen if the side rectangles were not all the same size?
3. How do you calculate the surface area of other types of prisms, like rectangular prisms?
4. If the prism were to be filled with a material, how could you calculate the volume?
5. How can you visualize a net of a prism in 3D?

Tip: Always break down the surface area into smaller, manageable parts like triangular and rectangular faces to simplify your calculations.