https://file.aiquickdraw.com/mathbot/file/1725752971141jiui8j79.jpg

 Find the total surface area of the all solid shown below.

The solid shown in the image is a **triangular prism** with dimensions provided for its triangular face and rectangular sides.

### Steps to find the total surface area:
1. **Surface Area Formula for a Triangular Prism:**
   \[
   \text{Total Surface Area} = 2 \times \text{Area of triangular base} + \text{Area of three rectangular faces}
   \]
   
2. **Area of the triangular base:**
   The triangle has base = 6 units, and height = 4 units (as indicated by the right triangle in the diagram).
   \[
   \text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   = \frac{1}{2} \times 6 \times 4 = 12 \text{ square units.}
   \]

3. **Area of the three rectangular faces:**
   The three rectangles correspond to the sides of the prism.
   - First rectangle: \(6 \times 7 = 42\) square units
   - Second rectangle: \(5 \times 7 = 35\) square units
   - Third rectangle: \(4 \times 7 = 28\) square units

4. **Total Surface Area Calculation:**
   \[
   \text{Total Surface Area} = 2 \times 12 + 42 + 35 + 28
   = 24 + 42 + 35 + 28 = 129 \text{ square units.}
   \]

Thus, the total surface area of the triangular prism is **129 square units**.

Would you like more details or clarifications on any of the steps?

### Relative Questions:
1. What is the surface area of a rectangular prism?
2. How does the surface area of a cylinder compare to that of a prism?
3. What is the volume of this triangular prism?
4. Can you calculate the lateral surface area of the prism?
5. How would the surface area change if the dimensions of the triangle were doubled?

### Tip:
For any prism, the total surface area includes both the base areas and the lateral faces. Always double-check the shape and dimensions to ensure correct surface area calculation!

Find the total surface area of the solid shown below.

Learn how to calculate the total surface area of a triangular prism with given dimensions. The solution involves calculating the area of the triangular base and the three rectangular faces. Ideal for students in Grades 6-8.

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