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 #3 #, its base has sides of length #4 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?

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Answer 1 · 2018-01-31T11:48:58

Total Surface Area of Pyramid #T S A = color(purple)(42.7008)#

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Area of rhombic base

#A_r = a * a sin theta = 4^2 sin ((2pi)/3) = color(green)(13.8564)#

Area of slant triangle #A_s = (1/2) a * l#

where #l = sqrt((a/2)^2 + h^2) = sqrt(2^2 + 3^2) = color(brown)(3.5056)#

Lateral Surface Area of the Pyramid

#A_l = 4 * A_s = 4 * (1/2) * 4 * 3.5056 = color(green)(28.8444)#

Total Surface Area of Pyramid
#T S A = A_r + A_l = 13.8564 + 28.8444 = color(purple)(42.7008)#