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 #2 #, its base's sides have lengths of #4 #, and its base has a corner with an angle of #( pi)/6 #. What is the pyramid's surface area?

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Answer 1 · 2018-02-20T04:54:46

T S A #color(blue)(A_T = A_b + A_l = 8 + 22.6274 = 30.6274# sq. units

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Pyramid total surface area = base area + lateral surface area

Base is a rhombus and hence #A_b = (d1 * d2)/2# or #a^2sin theta#

Lateral Surface area #A_l = 4 * (1/2) a l# where l is the slant height.

#A_b = 4a^2 sin (pi/6) = 8#

#l = sqrt ((a/2)^2 + h^2) = sqrt((4/2)^2 + 2^2) = 2.8284#

#A_l = 4 * (1/2) * 4 * 2.8284 = 22.6274#

#T S A #A_T = A_b + A_l = 8 + 22.6274 = 30.6274# sq. units