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's sides have lengths of #2 #, and its base has a corner with an angle of #(7 pi)/8 #. What is the pyramid's surface area?

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Answer 1 · 2018-07-23T09:55:52

Surface area of the pyramid # T S A = 29.815# sq. units.

Pyramid surface area = base area + lateral Surface area.

i. e. #T S A = A_b + L S A#

#A_b = 2^2 sin ((7pi)/8) = 1.5307# sq. units

Height of pyramid #= 7#

Slant height of lateral surface #s = sqrt((2/2)^2 + 7^2) = sqrt 50#

#L S A = 4 * ((1/2) * 2 * sqrt50) = 28.2843# sq. units.

#T S A = A_b + L S A = 1.5307 + 28.2843 = 29.815# sq. units.