Question

A rectangular prism has length of 2 feet, a width of 3 feet, and a height of 4 feet. What is the surface area of the rectangular prism? Draw a net to help you find your answer.(1 point)
how many square feet

Answer 1

To calculate the surface area of a rectangular prism, you can use the formula:

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

where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

In this case:
- \( l = 2 \) feet
- \( w = 3 \) feet
- \( h = 4 \) feet

Now, plug in the values:

1. Calculate \( 2lw \):
\[
2lw = 2 \times 2 \times 3 = 12 \, \text{square feet}
\]

2. Calculate \( 2lh \):
\[
2lh = 2 \times 2 \times 4 = 16 \, \text{square feet}
\]

3. Calculate \( 2wh \):
\[
2wh = 2 \times 3 \times 4 = 24 \, \text{square feet}
\]

Now, add all these areas together to find the total surface area:

\[
\text{Surface Area} = 12 + 16 + 24 = 52 \, \text{square feet}
\]

Therefore, the surface area of the rectangular prism is **52 square feet**.

### Drawing a Net
To visualize the surface area, you can imagine the net of the rectangular prism. The net consists of six rectangles, representing the faces of the prism.

Here’s a simple representation of the net:

```
+---------------+
| | (Top: 2 ft x 3 ft)
| |
+---------------+
| | (Front: 2 ft x 4 ft)
| |
+---------------+
+---------------+ +---------------+
| | | |
| | | | (Back: 2 ft x 4 ft)
+---------------+ +---------------+
| |
| | (Bottom: 2 ft x 3 ft)
+---------------+
```

The sides of the prism, which are each \( 3 \, \text{ft} \times 4 \, \text{ft} \), would also be represented in this net. The net includes all six faces, confirming the calculation we performed.