To find the total surface area of a rectangular box (also known as a rectangular prism), you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
For the given box:
- Length \( l = 3 \) feet
- Width \( w = 2 \) feet
- Height \( h = 4 \) feet
Now, we can calculate each term in the formula:
- \( lw = 3 \times 2 = 6 \)
- \( lh = 3 \times 4 = 12 \)
- \( wh = 2 \times 4 = 8 \)
Next, add those values together:
\[ lw + lh + wh = 6 + 12 + 8 = 26 \]
Now, multiply by 2 to find the total surface area:
\[ \text{Surface Area} = 2 \times 26 = 52 \text{ square feet} \]
Thus, the total surface area of the box is 52 square feet.