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The image you uploaded appears to show a composite figure made of a prism and a pyramid. The task is to calculate the total surface area (SA) of the composite shape. Here's how we can break it down:

### Information from the image:
1. **Pyramid (top part):**
   - Base: 3 cm by 3 cm (square base)
   - Slant height of the triangular faces: 5 cm
   - Given surface area (SA) of the pyramid: 54 cm²

2. **Prism (bottom part):**
   - Base: 6 cm by 3 cm (rectangular base)
   - Height: 10 cm
   - Given surface area (SA) of the prism: 198 cm²

The task is to find the total surface area of the composite figure.

### Solution steps:
- Since the base of the pyramid coincides with the top of the prism, this overlapping area should not be double-counted.
- The total surface area of the composite figure is the sum of the surface areas of the pyramid and the prism, minus the area of the overlapping base.

The formula for the total surface area (SA) is:
\[
SA_{\text{total}} = SA_{\text{pyramid}} + SA_{\text{prism}} - \text{Area of the base}
\]
Where:
- \(SA_{\text{pyramid}} = 54 \, \text{cm}^2\)
- \(SA_{\text{prism}} = 198 \, \text{cm}^2\)
- Area of the base of the pyramid (a square): \(3 \, \text{cm} \times 3 \, \text{cm} = 9 \, \text{cm}^2\)

Let's calculate the total surface area.The total surface area of the composite figure is \( 243 \, \text{cm}^2 \).

Would you like further details or explanations on this? Here are some related questions that might help extend your understanding:

1. How do you calculate the surface area of a rectangular prism?
2. What is the formula for the surface area of a pyramid?
3. How would the surface area change if the dimensions of the base of the pyramid and prism were different?
4. Can this method be applied to other 3D composite shapes?
5. What is the significance of subtracting the overlapping base area in surface area calculations?

**Tip:** When calculating surface areas of composite figures, always remember to subtract overlapping areas to avoid double-counting them!

Calculate the total surface area of a composite figure made up of a pyramid and a prism.

Learn how to calculate the total surface area of a composite figure made of a pyramid and a prism. This problem involves the subtraction of overlapping areas, applying the surface area formulas for both shapes. Ideal for students in Grades 6-8.

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