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 #4 #, its base's sides have lengths of #8 #, and its base has a corner with an angle of #(7 pi)/8 #. What is the pyramid's surface area?

1 Answer
Dec 12, 2017

T S A = 115.0021

Explanation:

AB = BC = CD = DA = a = 8
Height OE = h = 4
OF = a/2 = 8/2 = 4
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(4^2+4^2) = color(red)(5.6569)#

Area of #DCE = (1/2)*a*EF = (1/2)*8*5.6569 = color(red)(22.6276)#
Lateral surface area #= 4*Delta DCE = 4*22.6276 = color(blue)(90.5104)#

#/_C = (pi) - ((7pi)/8) = (pi)/8#
Area of base ABCD #= a* a * sin /_C = 8^2 sin (pi/8) = 24.4917#

T S A #= Lateral surface area + Base area#
T S A # =90.5104 + 24.4917 = color(purple)(115.0021)#

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