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 has sides of length #1 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?

1 Answer
Dec 20, 2017

T S A = 14.9016

Explanation:

AB = BC = CD = DA = a = 1
Height OE = h = 7
OF = a/2 = 1/2 = 0.5
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(7^2+0.5^2) = color(red)(7.0178)#

Area of #DCE = (1/2)*a*EF = (1/2)*1*7.0178 = color(red)(3.5089)#
Lateral surface area #= 4*Delta DCE = 4*3.5089 = color(blue)(14.0356)#

#/_C = pi - (2pi)/3 = (pi)/3#
Area of base ABCD #= a* a * sin /_C = 1^2 sin (pi/3) = 0.866#

T S A #= Lateral surface area + Base area#
T S A # =14.0356 + 0.866 = color(purple)(14.9016)#

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