https://file.aiquickdraw.com/mathbot/file/17303825055389k7s4r46.jpg

To find the surface area of this triangular prism, we’ll need to calculate the area of each face shown in the net diagram.

### Step 1: Calculate the Area of the Triangular Faces
The two triangular faces of the prism each have a base of \(10 \, \text{m}\) and a height of \(12 \, \text{m}\).

\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 12 = 60 \, \text{m}^2
\]

Since there are two identical triangular faces:
\[
\text{Total area of triangular faces} = 2 \times 60 = 120 \, \text{m}^2
\]

### Step 2: Calculate the Area of the Three Rectangular Faces
1. **First rectangle (connected to the 20 m side):**
   - Dimensions: \(20 \, \text{m} \times 10 \, \text{m}\)
   - Area: \(20 \times 10 = 200 \, \text{m}^2\)

2. **Second rectangle (connected to the 21 m side):**
   - Dimensions: \(21 \, \text{m} \times 10 \, \text{m}\)
   - Area: \(21 \times 10 = 210 \, \text{m}^2\)

3. **Third rectangle (connected to the 13 m side):**
   - Dimensions: \(13 \, \text{m} \times 10 \, \text{m}\)
   - Area: \(13 \times 10 = 130 \, \text{m}^2\)

Adding these areas together:
\[
\text{Total area of rectangular faces} = 200 + 210 + 130 = 540 \, \text{m}^2
\]

### Step 3: Add All Areas Together
\[
\text{Total surface area} = 120 + 540 = 660 \, \text{m}^2
\]

### Final Answer
The surface area of the prism is:
\[
660 \, \text{m}^2
\]

Would you like more details or have any questions about the steps?

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Here are some related questions for further understanding:
1. How would the surface area change if the height of the triangle increased?
2. What is the volume of this triangular prism?
3. How does the shape of the base affect the surface area calculation?
4. If one side length of the rectangular face changes, how does it affect the total surface area?
5. How would you find the surface area if the prism were hollow?

**Tip:** Always double-check each face’s dimensions to avoid errors in surface area calculations.

What is the surface area of the triangular prism shown in the image? Remember to give the correct units.

This solution walks through calculating the surface area of a triangular prism with a base of 10 meters and height of 12 meters. Includes step-by-step calculation of each face’s area to find the total surface area, suitable for students in Grades 6-8.

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