The question asks for the surface area of the shape shown in the image. The figure is a combination of a rectangular prism (cuboid) at the bottom and a pyramid on top. Here's how we can calculate the total surface area:

1. Surface Area of the Rectangular Prism (Cuboid)

The cuboid has three dimensions:

• Length $l = 32 \, \text{cm}$
• Width $w = 18 \, \text{cm}$
• Height $h = 10 \, \text{cm}$

The surface area of a cuboid is calculated by: $A_{\text{cuboid}} = 2(lw + lh + wh)$ Substitute the values: $A_{\text{cuboid}} = 2(32 \times 18 + 32 \times 10 + 18 \times 10)$ $A_{\text{cuboid}} = 2(576 + 320 + 180) = 2 \times 1076 = 2152 \, \text{cm}^2$

2. Surface Area of the Pyramid

The pyramid has a square base (since the length and width of the cuboid are different, we'll use the smaller base dimension), and the slant height of the pyramid is provided as $12 \, \text{cm}$.

The pyramid has four triangular faces, each with a base of $l = 32 \, \text{cm}$ and a slant height $s = 12 \, \text{cm}$. The area of one triangular face is: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{slant height}$ $A_{\text{triangle}} = \frac{1}{2} \times 32 \times 12 = 192 \, \text{cm}^2$ Since there are four triangular faces, the total surface area of the pyramid is: $A_{\text{pyramid}} = 4 \times 192 = 768 \, \text{cm}^2$

3. Total Surface Area

To find the total surface area, we add the surface areas of the cuboid and the pyramid: $A_{\text{total}} = A_{\text{cuboid}} + A_{\text{pyramid}} = 2152 + 768 = 2920 \, \text{cm}^2$

Thus, the correct answer is closest to Option D: 2916 cm².

Do you want further details or have any questions?

Here are 5 questions that can deepen your understanding:

1. How would the surface area change if the height of the pyramid increased?
2. How do you calculate the surface area of a cone?
3. How would you calculate the volume of this combined shape?
4. What is the difference between lateral and total surface area in 3D shapes?
5. How can we modify the shape to increase the surface area without changing the base dimensions?

Tip: When calculating surface area, always ensure to count all exposed faces carefully to avoid errors.