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's sides have lengths of #2 #, and its base has a corner with an angle of #( pi)/4 #. What is the pyramid's surface area?

1 Answer
Dec 25, 2017

T S A = 31.1128

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 - (3pi)/4 = (pi)/4#
Area of base ABCD #= a* a * sin /_C = 2^2 sin (pi/4) = 2.8284#

T S A #= Lateral surface area + Base area#
T S A # =28.2844 + 2.8284 = color(purple)(31.1128)#

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