To calculate the surface area of a prism with a square base, we can use the following formula:
\[ \text{Surface Area} = 2 \times (\text{Base Area}) + \text{Lateral Area} \]
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Calculate the base area:
- The base is a square with a side length of \(8\) inches.
- Base Area = side length × side length = \(8 \text{ in.} \times 8 \text{ in.} = 64 \text{ in.}^2\).
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Find the total area of the two bases:
- Since there are two bases, we multiply the base area by 2:
- Base Area (2 bases) = \(2 \times 64 \text{ in.}^2 = 128 \text{ in.}^2\).
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Calculate the lateral area:
- The lateral area is the perimeter of the base multiplied by the height of the prism.
- Perimeter of the square base = \(4 \times \text{side length} = 4 \times 8 \text{ in.} = 32 \text{ in.}\).
- Lateral Area = Perimeter × Height = \(32 \text{ in.} \times 20 \text{ in.} = 640 \text{ in.}^2\).
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Calculate the total surface area:
- Add the area of the bases and the lateral area:
- Total Surface Area = Base Area (2 bases) + Lateral Area = \(128 \text{ in.}^2 + 640 \text{ in.}^2 = 768 \text{ in.}^2\).
So the correct surface area of the prism is:
768 in².