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 #4 #, its base has sides of length #8 #, and its base has a corner with an angle of #(3 pi)/4 #. What is the pyramid's surface area?

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Answer 1 · 2018-01-11T05:42:53

#T S A = color(red)(135.7652)#

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Pyramid height #h = 4#, Rhombus side #l = 8#

Area of rhombus base #A_r = l * l* sin theta = 8^2 sin ((3pi)/4) = color(blue)(45.2548)#

Area of slant triangle #A_t = (1/2) l * H#

where slant height

#H = sqrt (h^2 + (l/2)l^2) = sqrt(4^2 + (8/2)^2) = 5.6569#

#L S A = 4 * A_t = 4 * (1/2) * 8 * 5.6569 = color(blue)(90.5104)#

#T S A = A_r + L S A = 45.2548 + 90.5104 = color(red)(135.7652)#