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's sides have lengths of #9 #, and its base has a corner with an angle of #(5 pi)/8 #. What is the pyramid's surface area?

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Answer 1 · 2018-06-10T05:55:52

#color(purple)(T S A " of Pyramid " A_p = 74.83 + 121.08 = 195.91#

#"Surface Area of Pyramid = Area of rhombus base + Area of 4 slant triangles#

#A_p = A_b + 4 A_s#

#b = 9, theta = (5pi)/8, h = 5#

#A_b = b^2 sin theta = 9^2 sin ((5pi)/8) = 74.83#

#4 * A_s = 4 * ((1/2) * b * l ) = 2 * 9 * sqrt((9/2)^2 + 5^2)#

#4 A_s = 121.08#

#color(purple)(T S A " of Pyramid " A_p = 74.83 + 121.08 = 195.91#