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

1 Answer
Dec 12, 2017

T S A = 33.9409

Explanation:

AB = BC = CD = DA = a = 4
Height OE = h = 2
OF = a/2 = 4/2 = 2
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(2^2+2^2) = color(red)(2.8284)#

Area of #DCE = (1/2)*a*EF = (1/2)*4*2.8284 = color(red)(5.6568)#
Lateral surface area #= 4*Delta DCE = 4*5.6568 = color(blue)(22.6272)#

#/_C = (pi)/4#
Area of base ABCD #= a* a * sin /_C = 4^2 sin (pi/4) = 11.3137#

T S A #= Lateral surface area + Base area#
T S A # =22.6272 + 11.3137 = color(purple)(33.9409)#

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