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

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Answer 1 · 2017-12-12T13:11:56

T S A = 35.7132

AB = BC = CD = DA = a = 2
Height OE = h = 8
OF = a/2 = 2/2 = 1
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(8^2+1^2) = color(red)(8.0623)#

Area of #DCE = (1/2)*a*EF = (1/2)*2*8.0623 = color(red)(8.0623)#
Lateral surface area #= 4*Delta DCE = 4*8.0623 = color(blue)(32.2492)#

#/_C = pi - (2pi)/3 = (pi)/3#
Area of base ABCD #= a* a * sin /_C = 2^2 sin (pi/3) = 3.464#

T S A #= Lateral surface area + Base area#
T S A # =32.2492 + 3.464 = color(purple)(35.7132)#

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