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:
-
Calculate \( 2lw \): \[ 2lw = 2 \times 2 \times 3 = 12 , \text{square feet} \]
-
Calculate \( 2lh \): \[ 2lh = 2 \times 2 \times 4 = 16 , \text{square feet} \]
-
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.