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 #9 #, 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 · 2018-06-30T06:02:42

color(green )(A_p = A_b + L S A = 8 + 18.44 = 26.44# sq units

Pyramid’s Surface Area #A_p = A_b + L S A#

where #A_b = s^2 sin theta, L S A = 4 * (1/2) s sqrt((s/2)^2 + h^2)#

Given #s = 4, h = 9, theta = (pi)/6#

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

#L S A = 4 * (1/2) *4 * sqrt((4/2)^2 + 9^2) ~~ 18.44#

#color(green )(A_p = A_b + L S A = 8 + 18.44 = 26.44# sq units