The given shape is a rectangular prism with a triangular prism as its roof. To calculate the surface area, we need to find the areas of all its faces and sum them up.

Step-by-step process:

1. Rectangular Prism (Bottom part): The rectangular prism has three pairs of rectangular faces:

   • Two rectangles on the front and back (width = 7 cm, height = 4 cm)
   • Two rectangles on the sides (length = 8 cm, height = 4 cm)
   • Two rectangles on the top and bottom (width = 7 cm, length = 8 cm)

2. Triangular Prism (Roof part): The triangular prism has the following:

   • Two triangular faces (height = 3 cm, base = 7 cm)
   • Two rectangular faces (side walls of the roof, each with length = 8 cm, height = 5 cm, which is the slant height of the triangle)
   • One rectangular face (base of the triangular prism, width = 7 cm, length = 8 cm)

Step-by-step calculation:

1. Area of the rectangular prism (bottom part):

• Front and back: $2 \times (7 \times 4) = 2 \times 28 = 56 \, \text{cm}^2$
• Side faces: $2 \times (8 \times 4) = 2 \times 32 = 64 \, \text{cm}^2$
• Top and bottom: $2 \times (7 \times 8) = 2 \times 56 = 112 \, \text{cm}^2$

2. Area of the triangular prism (roof part):

• Two triangular faces: $2 \times \left(\frac{1}{2} \times 7 \times 3\right) = 2 \times 10.5 = 21 \, \text{cm}^2$
• Two rectangular side faces (slanted walls): $2 \times (8 \times 5) = 2 \times 40 = 80 \, \text{cm}^2$
• One rectangular face (base of the roof): $7 \times 8 = 56 \, \text{cm}^2$

Total Surface Area:

Summing all the areas calculated: $56 + 64 + 112 + 21 + 80 + 56 = 389 \, \text{cm}^2$

Thus, the total surface area of the prism is 389 cm².

Let me know if you need any further details, or feel free to ask about the following:

1. How would the surface area change if the triangular height increased?
2. What formula is used to calculate the slant height of the triangular prism?
3. How is the volume of this composite figure calculated?
4. How would painting this figure affect the surface area calculations?
5. What are the common uses of prisms like this in real-world applications?

Tip: Always break down complex shapes into simpler parts to calculate surface area or volume.