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 #6 #, its base's sides have lengths of #2 #, and its base has a corner with an angle of #( pi)/4 #. What is the pyramid's surface area?

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Answer 1 · 2018-06-21T12:04:35

#color(brown)(T S A = A_b + L S A = 2.83 + 24.32 = 27.15 " sq units"#

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#h = 6, a = 2, theta = pi/4#

#"Area of base " = A_b = a^2 sin theta = 2^2 sin ((pi/4) = 2.83#

#"Slant height " = l = sqrt((a/2)^2 + h^2) = sqrt((2/2)^2 + 6^2) = 6.08#

#"Lateral Surface Area " = L S A = 4 * (1/2) * a * l = 2 * 2 * 6.08 = 24.32#

#color(brown)(T S A = A_b + L S A = 2.83 + 24.32 = 27.15 " sq units"#