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 #6 #, its base has sides of length #1 #, and its base has a corner with an angle of #(3 pi)/8 #. What is the pyramid's surface area?

1 Answer
sankarankalyanam
Dec 20, 2017

T S A = 12.9655

Explanation:

AB = BC = CD = DA = a = 1
Height OE = h = 6
OF = a/2 = 1/2 = 0.5
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(6^2+0.5^2) = color(red)(6.0208)#

Area of #DCE = (1/2)*a*EF = (1/2)*1*6.0208 = color(red)(3.0104)#
Lateral surface area #= 4*Delta DCE = 4*3.0104 = color(blue)(12.0416)#

#/_C = (3pi)/8#
Area of base ABCD #= a* a * sin /_C = 1^2 sin (3pi/8) = 0.9239#

T S A #= Lateral surface area + Base area#
T S A # =12.0416 + 0.9239 = color(purple)(12.9655)#

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