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

1 Answer
Dec 12, 2017

T S A = 31.9244

Explanation:

AB = BC = CD = DA = a = 2
Height OE = h = 7
OF = a/2 = 2/2 = 1
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(7^2+1^2) = color(red)(7.0711)#

Area of #DCE = (1/2)*a*EF = (1/2)*2*7.0711 = color(red)(7.0711)#
Lateral surface area #= 4*Delta DCE = 4*7.0711 = color(blue)(28.2844)#

#/_C = (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 # =28.2844 + 3.464 = color(purple)(31.9244)#

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