To calculate the surface area of a rectangular prism, you can use the following formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length (\( l \)) = 2 feet
- Width (\( w \)) = 3 feet
- Height (\( h \)) = 4 feet
Now, we can substitute these values into the formula:
-
Calculate the areas of each pair of opposite faces:
- Area of length and width faces: \( lw = 2 \times 3 = 6 \) square feet (there are 2 of these)
- Area of length and height faces: \( lh = 2 \times 4 = 8 \) square feet (there are 2 of these)
- Area of width and height faces: \( wh = 3 \times 4 = 12 \) square feet (there are 2 of these)
-
Substitute the values into the surface area formula: \[ \text{Surface Area} = 2(6 + 8 + 12) \] \[ \text{Surface Area} = 2(26) \] \[ \text{Surface Area} = 52 \text{ square feet} \]
The surface area of the rectangular prism is 52 square feet.
Drawing a Net
To visualize the dimensions and understand the surface area calculation better, you can draw a net of the rectangular prism. The net of a rectangular prism looks like this:
+-------------+
| |
| Top | 2 ft
| |
+-------------+
| |
| Front | 4 ft
| |
+-----+-------------+-----+
| (l) |
| Bottom | | 3 ft
| (w) |
+-----+-------------+-----+
| |
| Back | 4 ft
| |
+-------------+
| |
| Right | 3 ft
| |
+-------------+
This net can help you visualize how the sides come together to form the rectangular prism and reinforces how each pair of opposite rectangles contributes to the total surface area.