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 #8 #, its base has sides of length #2 #, and its base has a corner with an angle of #(3 pi)/8 #. What is the pyramid's surface area?

1 Answer
Dec 12, 2017

T S A = 35.9447

Explanation:

AB = BC = CD = DA = a = 2
Height OE = h = 8
OF = a/2 = 2/2 = 1
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(8^2+1^2) = color(red)(8.0623)#

Area of #DCE = (1/2)*a*EF = (1/2)*2*8.0623 = color(red)(8.0623)#
Lateral surface area #= 4*Delta DCE = 4*8.0623 = color(blue)(32.2492)#

#/_C = (3pi)/8#
Area of base ABCD #= a* a * sin /_C = 2^2 * sin (3pi)/8 = 3.6955#

T S A #= Lateral surface area + Base area#
T S A # =32.2492 + 3.6955 = color(purple)(35.9447)#

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