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

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Answer 1 · 2018-06-29T08:11:45

#color(cyan)(T S A = 56.63 " sq units"#

#"Area of rhombus base ' + A_r = s^2 * sin (pi/3) = 3^2 * (sqrt3/2) = 7.79#

#"Slant height of the pyramid " l = sqrt((3/2)^2 + 8^2) = 8.1394#

#"Lateral Surface Area of Pyramid " L S A = 4 * (1/2) * s * l#

#L S A = 4 * (1/2) * 3 * 8.1394 = 48.84#

#"Total Surface Area of Pyramid ' = T S A = A_b + L S A #

#T S A = 7.79 + 48.84 = 56.63 " sq units"#