Sure! Let's find the surface area of the given rectangular prism step by step.
The formula for the surface area [tex]\(S\)[/tex] of a rectangular prism with length [tex]\(l\)[/tex], width [tex]\(w\)[/tex], and height [tex]\(h\)[/tex] is:
[tex]\[ S = 2lw + 2lh + 2wh \][/tex]
Given:
- Length ([tex]\(l\)[/tex]) = 6.2 yards
- Width ([tex]\(w\)[/tex]) = 3.15 yards
- Height ([tex]\(h\)[/tex]) = 44 yards
Let's compute each term in the formula separately:
1. Calculate [tex]\(2lw\)[/tex]:
[tex]\[ 2lw = 2 \times 6.2 \times 3.15 \][/tex]
[tex]\[ 2lw = 2 \times 19.53 \][/tex]
[tex]\[ 2lw = 39.06 \][/tex]
2. Calculate [tex]\(2lh\)[/tex]:
[tex]\[ 2lh = 2 \times 6.2 \times 44 \][/tex]
[tex]\[ 2lh = 2 \times 272.8 \][/tex]
[tex]\[ 2lh = 545.6 \][/tex]
3. Calculate [tex]\(2wh\)[/tex]:
[tex]\[ 2wh = 2 \times 3.15 \times 44 \][/tex]
[tex]\[ 2wh = 2 \times 138.6 \][/tex]
[tex]\[ 2wh = 277.2 \][/tex]
Now, sum up all the terms to find the total surface area:
[tex]\[ S = 2lw + 2lh + 2wh \][/tex]
[tex]\[ S = 39.06 + 545.6 + 277.2 \][/tex]
[tex]\[ S = 861.86 \][/tex]
Finally, we round the result to the nearest hundredth:
The surface area of the rectangular prism is [tex]\( \boxed{861.86} \)[/tex] square yards.
