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 7 7, its base has sides of length 1 1, and its base has a corner with an angle of (2 pi)/3 2π3. What is the pyramid's surface area?

1 Answer
sankarankalyanam
Dec 20, 2017

T S A = 14.9016

Explanation:

AB = BC = CD = DA = a = 1
Height OE = h = 7
OF = a/2 = 1/2 = 0.5
EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(7^2+0.5^2) = color(red)(7.0178)EF=√EO2+OF2=√h2+(a2)2=√72+0.52=7.0178

Area of DCE = (1/2)*a*EF = (1/2)*1*7.0178 = color(red)(3.5089)DCE=(12)⋅a⋅EF=(12)⋅1⋅7.0178=3.5089
Lateral surface area = 4*Delta DCE = 4*3.5089 = color(blue)(14.0356)

/_C = pi - (2pi)/3 = (pi)/3
Area of base ABCD = a* a * sin /_C = 1^2 sin (pi/3) = 0.866

T S A = Lateral surface area + Base area
T S A =14.0356 + 0.866 = color(purple)(14.9016)

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