To find the total surface area of a rectangular prism (in this case, the dog crate), you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- \( l = 4 \) feet
- \( w = 2 \) feet
- \( h = 3.5 \) feet
Now, substituting the values into the formula:
\[ lw = 4 \times 2 = 8 \quad \text{(Area of the bottom/top)} \] \[ lh = 4 \times 3.5 = 14 \quad \text{(Area of the front/back)} \] \[ wh = 2 \times 3.5 = 7 \quad \text{(Area of the sides)} \]
Now, summing these areas:
\[ lw + lh + wh = 8 + 14 + 7 = 29 \]
Now, calculating the total surface area:
\[ \text{Surface Area} = 2 \times 29 = 58 \text{ square feet} \]
So, the total surface area of the dog crate is 58 square feet.