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 #7 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?

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Answer 1 · 2018-01-22T13:50:43

Total Surface Area #A_T = color(green)(127.8812)#

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Given #l = 7, h = 5#
Area of Rhombus base #A_R = l * l sin (theta)#

#A_R = 7^2 sin ((2pi)/3) ~~42.4352#

Area of one slant triangle

#A_t =(1/2)( l * sqrt ((l/2)^2 + h^2))#

#A_t =(1/2) ( 7 * sqrt((3.5)^2 + 5^2) )= 21.3615#

Total Surface Area #A_T = A_R + (4 * A_t)#

#A_T = 42.4352 + (4 * 21.3615) = color(green)(127.8812)#