A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is 8 8, its base has sides of length 7 7, and its base has a corner with an angle of (3 pi)/8 3π8. What is the pyramid's surface area?

1 Answer
sankarankalyanam
Dec 12, 2017

T S A = 167.5196

Explanation:

AB = BC = CD = DA = a = 7
Height OE = h = 8
OF = a/2 = 7/2 = 3.5
EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(8^2+3.5^2) = color(red)(8.7321)EF=√EO2+OF2=√h2+(a2)2=√82+3.52=8.7321

Area of DCE = (1/2)*a*EF = (1/2)*7*8.7321 = color(red)(30.5624)DCE=(12)⋅a⋅EF=(12)⋅7⋅8.7321=30.5624
Lateral surface area = 4*Delta DCE = 4*30.5624 = color(blue)(122.2496)

/_C = (3pi)/8
Area of base ABCD = a* a * sin /_C = 7^2 sin ((3pi)/8) = 45.2701

T S A = Lateral surface area + Base area
T S A =122.2496 + 45.2701 = color(purple)(167.5196)

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