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A tower is composed of a prism with a square base and a pyramid. The base length is 20 meters, and the height of the prism is 40 meters, while the slant height of the pyramid is 10√2 meters. What is the total surface area, including the bottom base?
400√2 + 3,600 m2
200√2 + 3,600 m2
400√2 + 400 m2
4000√2 m2
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Base side s = 20, prism height = 40, pyramid slant height l = 10√2.
Pyramid lateral area = 4 * (1/2 * s * l) = 4 * (1/2 * 20 * 10√2) = 400√2 m².
Prism lateral area = perimeter * height = (4*20) * 40 = 3200 m².
Bottom base area = 20*20 = 400 m².
Total surface area = 400√2 + 3200 + 400 = 400√2 + 3600 m².
Answer: 400√2 + 3,600 m².
Pyramid lateral area = 4 * (1/2 * s * l) = 4 * (1/2 * 20 * 10√2) = 400√2 m².
Prism lateral area = perimeter * height = (4*20) * 40 = 3200 m².
Bottom base area = 20*20 = 400 m².
Total surface area = 400√2 + 3200 + 400 = 400√2 + 3600 m².
Answer: 400√2 + 3,600 m².
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