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 #2 #, 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 · 2018-01-10T08:23:32

Total Surface Area of the pyramid with rhombus base

#T S A = color (purple)(12.8136)#

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Area of base #A_b = a^2 sin ((theta) = 2^2 sin ((3pi)/4) =color(blue)(0.1644)#

Lateral surface area #A_l#= area of the four triangles.

Area of triangle #A_t = (1/2) a H# where H is the slant height of the lateral surface.

#H = sqrt(h^2 + (a/2)^2) = sqrt(3^2 + 1^2) = 3.1623#

L S A #A_l = 4 * (1/2) a * H = 4 * (1/2) * 2 * 3.1623 = color (blue)(12.6492)#

#T S A = A_b + A_l = 0.1644 + 12.6492 = color(purple)(12.8136)#