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 9 9, its base has sides of length 6 6, and its base has a corner with an angle of pi/4 π4. What is the pyramid's surface area?

1 Answer
sankarankalyanam
Dec 12, 2017

T S A = 139.2936

Explanation:

AB = BC = CD = DA = a = 6
Height OE = h = 9
OF = a/2 = 6/2 = 103
EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(9^2+3^2) = color(red)(9.4868)EF=√EO2+OF2=√h2+(a2)2=√92+32=9.4868

Area of DCE = (1/2)*a*EF = (1/2)*6*9.4868 = color(red)(28.4604)DCE=(12)⋅a⋅EF=(12)⋅6⋅9.4868=28.4604
Lateral surface area = 4*Delta DCE = 4*28.4604 = color(blue)(113.8416)

/_C = (pi)/4
Area of base ABCD = a* a * sin /_C = 6^2 sin (pi/4) = 25.452

T S A = Lateral surface area + Base area
T S A =113.8416 + 25.452 = color(purple)(139.2936)

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