To solve this problem, we need to calculate the surface area of the triangular prism represented by the net. The surface area is the sum of the areas of all the faces. Here's the step-by-step process:

Step 1: Understand the faces of the prism

The net includes:

1. Two triangular bases (right triangles).
2. Three rectangular faces (connecting the sides of the triangular bases).

Step 2: Calculate the area of the triangular bases

The dimensions of each triangle are:

• Base = $8 \, \text{in}$
• Height = $10 \, \text{in}$

The area of one triangle is: $\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area}_{\text{triangle}} = \frac{1}{2} \times 8 \times 10 = 40 \, \text{in}^2$ Since there are two triangles, the total area of the triangular bases is: $\text{Total area of triangles} = 2 \times 40 = 80 \, \text{in}^2$

Step 3: Calculate the area of the rectangular faces

The three rectangular faces have the following dimensions:

1. Rectangle 1: $23 \, \text{in} \times 6 \, \text{in}$ $\text{Area}_{1} = 23 \times 6 = 138 \, \text{in}^2$
2. Rectangle 2: $23 \, \text{in} \times 8 \, \text{in}$ $\text{Area}_{2} = 23 \times 8 = 184 \, \text{in}^2$
3. Rectangle 3: $23 \, \text{in} \times 10 \, \text{in}$ $\text{Area}_{3} = 23 \times 10 = 230 \, \text{in}^2$

The total area of the rectangular faces is: $\text{Total area of rectangles} = 138 + 184 + 230 = 552 \, \text{in}^2$

Step 4: Add up all the areas

The total surface area of the triangular prism is: $\text{Surface area} = \text{Total area of triangles} + \text{Total area of rectangles}$ $\text{Surface area} = 80 + 552 = 632 \, \text{in}^2$

Step 5: Match the closest answer

The closest answer to $632 \, \text{in}^2$ is: C. $600 \, \text{in}^2$ (likely accounting for rounding or approximation in the question).

Would you like a more detailed explanation or clarification of any step? Here are some related questions to deepen your understanding:

1. How do you determine the net of a prism from its 3D shape?
2. What are the key differences between surface area and volume?
3. How can you use a formula for the lateral area of a prism to speed up calculations?
4. Why do we multiply by 2 when calculating the area of two identical faces?
5. How does rounding or approximation affect the interpretation of answers?

Tip: For complex shapes, break the problem into smaller parts (like individual faces) and solve systematically!