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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 #, its base has sides of length #9 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?

Answer 1

T S A = 219.9389

AB = BC = CD = DA = a = 9
Height OE = h = 7
OF = a/2 = 9/2 = 4.5
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(7^2+4.5^2) = color(red)(8.3217)#

Area of #DCE = (1/2)*a*EF = (1/2)*9*8.3217 = color(red)(37.4477)#
Lateral surface area #= 4*Delta DCE = 4*37.4477 = color(blue)(149.7908)#

#/_C = pi - (2pi)/3 = (pi)/3#
Area of base ABCD #= a* a * sin /_C = 9^2 * sin (pi/3) = 70.1481#

T S A #= Lateral surface area + Base area#
T S A # =149.7908 + 70.1481 = color(purple)(219.9389)#

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Answer 2

Caroline Aucoin

The surface area of the pyramid is ( 81\sqrt{3} + 54\sqrt{3} = 135\sqrt{3} ) square units.

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Answer from HIX Tutor

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