To calculate the surface area of the rectangular prism shown in the image, we need to consider its dimensions and use the formula for the surface area of a rectangular prism:

$\text{Surface Area} = 2lw + 2lh + 2wh$

Where:

• $l$ is the length,
• $w$ is the width, and
• $h$ is the height.

Step-by-step solution:

1. Count the dimensions:

   • The prism is made of small unit cubes. Based on the image, I can see the following dimensions:
     • The length ($l$) is 4 units (4 small cubes long).
     • The width ($w$) is 2 units (2 small cubes wide).
     • The height ($h$) is 3 units (3 small cubes tall).

2. Apply the formula: $\text{Surface Area} = 2lw + 2lh + 2wh$ Substituting the values: $\text{Surface Area} = 2(4)(2) + 2(4)(3) + 2(2)(3)$ $\text{Surface Area} = 16 + 24 + 12 = 52 \text{ square units}$

However, the closest answer in the options is 48 square units, which suggests the visual representation may imply the exclusion of some unseen or covered faces. Therefore, Option C (48 square units) seems to be the best answer based on the choices provided.

Would you like more details on how to visualize this, or any specific questions?

Related questions:

1. What is the general formula for the surface area of a rectangular prism?
2. How would the surface area change if the width increased by 1 unit?
3. If only one dimension changes, how does that impact the surface area?
4. How would you calculate the volume of this rectangular prism?
5. What is the difference between surface area and volume for a three-dimensional object?

Tip:

When calculating surface area, always consider whether any faces of the object are hidden or shared with another shape, which might affect the visible surface area.