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To calculate the total surface area of the given 3D shape, which appears to be a prism with a triangular cross-section, we will follow these steps:

1. **Breakdown of the prism's surfaces**:
   - **Two triangular faces** (front and back).
   - **Three rectangular faces** (base, side, and slanted top).

### Step 1: Area of the triangular faces
The triangle's base is 8 cm, and its height is 6 cm.
The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
A_{\text{triangle}} = \frac{1}{2} \times 8 \times 6 = 24 \, \text{cm}^2
\]
Since there are two identical triangular faces, their combined area is:
\[
\text{Total area of triangular faces} = 2 \times 24 = 48 \, \text{cm}^2
\]

### Step 2: Area of the rectangular faces
- **Bottom face**: The bottom face is a rectangle with dimensions 8 cm by 3 cm.
  \[
  A_{\text{bottom}} = 8 \times 3 = 24 \, \text{cm}^2
  \]

- **Side face**: This is a rectangle with dimensions 4 cm by 3 cm.
  \[
  A_{\text{side}} = 4 \times 3 = 12 \, \text{cm}^2
  \]

- **Slanted face**: This rectangle has a length of 10 cm (the slant height of the triangular face) and a width of 3 cm.
  \[
  A_{\text{slanted}} = 10 \times 3 = 30 \, \text{cm}^2
  \]

### Step 3: Total surface area
Now, summing all the areas:
\[
\text{Total surface area} = 48 + 24 + 12 + 30 = 114 \, \text{cm}^2
\]

Thus, the total surface area of the prism is **114 cm²**.

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you calculate the volume of this triangular prism?
2. How would the surface area change if the slanted height increased by 2 cm?
3. What is the significance of the slant height in triangular prisms?
4. How would the surface area be affected if the base width increased by 1 cm?
5. Can you explain how the formula for the area of a triangle is derived?

### Tip:
When calculating surface area, always break the shape into its simpler components (rectangles, triangles) and calculate each area separately before summing them up.

Learn how to calculate the total surface area of a triangular prism with a base of 8 cm, height of 6 cm, and slant height of 10 cm. The step-by-step solution covers important geometry concepts, including the area of triangles and rectangles. Suitable for students in Grades 6-8.

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