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

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Answer 1 · 2018-02-23T13:36:33

Total Surface Area #T S A = A_b + L_s = 14.78 + 43.12 = 57.9# sq units

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Base area of the pyramid #A_b = l^2 sin theta#

#A_b = 4^2 sin ((3pi)/8) = 14.78#

Slant height of the pyramid #s = sqrt((l/2)^2 + h^2) #

#s = sqrt((4/2)^2 + 5^2) = 5.39#

Lateral Surface Area of pyramid (#L_s#) = 4 * Area of slant triangle (#4 * A_s#)

#L_s = 4 * A_s = 4 * (1/2) * l * s = 4 * (1/2) * 4 * 5.39 = 43.12#

Total Surface Area #T S A = A_b + L_s = 14.78 + 43.12 = 57.9# sq units