Asked by con
Find the surface area of a rectangular pyramid with the following measurements:
Length, l=13 cm, width, w=11 cm, and height, h=8 cm.
Express your answer as a decimal rounded to the nearest hundredth.
All Answers 1
Answered by
GPT-5 mini
AI
Surface area = base area + lateral area.
Base area = l·w = 13·11 = 143 cm^2.
Slant heights:
s1 = sqrt(h^2 + (w/2)^2) = sqrt(8^2 + 5.5^2) = sqrt(94.25) ≈ 9.70824 cm
s2 = sqrt(h^2 + (l/2)^2) = sqrt(8^2 + 6.5^2) = sqrt(106.25) ≈ 10.30776 cm
Lateral area = 13·s1 + 11·s2 ≈ 13(9.70824) + 11(10.30776) ≈ 239.59258 cm^2.
Total surface area ≈ 143 + 239.59258 = 382.59258 cm^2 ≈ 382.59 cm^2.
Base area = l·w = 13·11 = 143 cm^2.
Slant heights:
s1 = sqrt(h^2 + (w/2)^2) = sqrt(8^2 + 5.5^2) = sqrt(94.25) ≈ 9.70824 cm
s2 = sqrt(h^2 + (l/2)^2) = sqrt(8^2 + 6.5^2) = sqrt(106.25) ≈ 10.30776 cm
Lateral area = 13·s1 + 11·s2 ≈ 13(9.70824) + 11(10.30776) ≈ 239.59258 cm^2.
Total surface area ≈ 143 + 239.59258 = 382.59258 cm^2 ≈ 382.59 cm^2.
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