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.