A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of $8$ $8$ and $6$ $6$ and the pyramid's height is $9$ $9$ . If one of the base's corners has an angle of $\frac{5 π}{12}$ $(5pi)/12$ , what is the pyramid's surface area?

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A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of $8$ $8$ and $6$ $6$ and the pyramid's height is $9$ $9$ . If one of the base's corners has an angle of $\frac{5 π}{12}$ $(5pi)/12$ , what is the pyramid's surface area?

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Answer 1 · 2017-10-18T18:37:40

Total surface area $= 168.7614$ $= 168.7614$

Explanation:

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$C H = 6 \cdot sin (\frac{5 π}{12}) = 5.7956$ $CH = 6*sin ((5pi)/12) = 5.7956$
Area of parallelogram base $= a \cdot b 1 = 6 \cdot 5.7956 = 33.7736$ $= a* b1 = 6* 5.7956=33.7736$

$E F = h_{1} = \sqrt{h^{2} + {(\frac{a}{2})}^{2}} = \sqrt{9^{2} + 4^{2}} = \sqrt{97}$ $EF = h_1 = sqrt(h^2 + (a/2)^2) = sqrt(9^2 + 4^2) = sqrt97$
Area of $Delta AEF = BEC = (1/2)*b*h_1 = (1/2)*6*sqrt97=3sqrt97$

$EG = h_2 = sqrt(h^2+(b/2)^2 = sqrt(9^2 + 3^2 = sqrt90$
Area of $Delta = CED = AEC = (1/2)*a*h_2 = (1/2)*8*sqrt90=4sqrt90$

Lateral surface area = $2* DeltaAED + 2*Delta CED$
$= 2*3sqrt97 + 2*4sqrt90 = 59.0931 + 75.8947 = 134.9878$

Total surface area =Area of parallelogram base + Lateral surface area $= 33.7736 + 134.9878 =168.7614$

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A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of $8$ $8$ and $6$ $6$ and the pyramid's height is $9$ $9$ . If one of the base's corners has an angle of $\frac{5 π}{12}$ $(5pi)/12$ , what is the pyramid's surface area?

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A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of 8 88 and 6 66 and the pyramid's height is 9 99 . If one of the base's corners has an angle of (5pi)/125π12(5pi)/12, what is the pyramid's surface area?

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A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of $8$ $8$ and $6$ $6$ and the pyramid's height is $9$ $9$ . If one of the base's corners has an angle of $\frac{5 π}{12}$ $(5pi)/12$ , what is the pyramid's surface area?