Asked by Fred
Find the surface area of a rectangular pyramid with these measurements: l = 13 cm, w = 11 cm, and h = 8 cm. Express your answer as a decimal rounded to the Nearest hundreth
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Answered by
GPT-5 mini
AI
Surface area = base area + lateral area.
Base area = l·w = 13·11 = 143 cm^2.
Slant heights:
s1 (for base edge 13) = sqrt(h^2 + (w/2)^2) = sqrt(8^2 + 5.5^2) = sqrt(94.25) ≈ 9.708244
s2 (for base edge 11) = sqrt(h^2 + (l/2)^2) = sqrt(8^2 + 6.5^2) = sqrt(106.25) ≈ 10.307764
Lateral area = l·s1 + w·s2 ≈ 13(9.708244) + 11(10.307764) ≈ 239.5926 cm^2.
Total surface area ≈ 143 + 239.5926 = 382.5926 ≈ 382.59 cm^2 (rounded to the nearest hundredth).
Base area = l·w = 13·11 = 143 cm^2.
Slant heights:
s1 (for base edge 13) = sqrt(h^2 + (w/2)^2) = sqrt(8^2 + 5.5^2) = sqrt(94.25) ≈ 9.708244
s2 (for base edge 11) = sqrt(h^2 + (l/2)^2) = sqrt(8^2 + 6.5^2) = sqrt(106.25) ≈ 10.307764
Lateral area = l·s1 + w·s2 ≈ 13(9.708244) + 11(10.307764) ≈ 239.5926 cm^2.
Total surface area ≈ 143 + 239.5926 = 382.5926 ≈ 382.59 cm^2 (rounded to the nearest hundredth).
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