To find the surface area of a rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \(l\), \(w\), and \(h\) represent the length, width, and height of the prism.
Given the dimensions of the rectangular prism:
- Length \(l = 334 , \text{dm}\)
- Width \(w = 412 , \text{dm}\)
- Height \(h = 5 , \text{dm}\)
Now, we can calculate each area component:
- \(lw = 334 \times 412\)
- \(lh = 334 \times 5\)
- \(wh = 412 \times 5\)
Now, calculate each of these:
- \(lw = 334 \times 412 = 137768 , \text{dm}^2\)
- \(lh = 334 \times 5 = 1670 , \text{dm}^2\)
- \(wh = 412 \times 5 = 2060 , \text{dm}^2\)
Now, sum these three areas:
\[ lw + lh + wh = 137768 + 1670 + 2060 = 140498 , \text{dm}^2 \]
Now, multiply by 2 to find the surface area:
\[ \text{Surface Area} = 2 \times 140498 = 280996 , \text{dm}^2 \]
So, the surface area of the rectangular prism is 280996 dm².
Since none of the provided responses match this value, it appears there may have been an error in the problem or the options listed.