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 #2 #, 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 · 2018-07-03T02:35:06

#color(brown)(Surface Area of the pyramid = 23.86 " sq units"#

#h = 5, a = 2, theta = pi/3#

#"Area of base " = A_b = a^2 sin theta = 2^2 sin ((pi/3) = 2 sqrt3 = 3.464#

#"Slant height " = l = sqrt((a/2)^2 + h^2) = sqrt((2/2)^2 + 5^2) = sqrt 26 = 5.099#

#"Lateral Surface Area " = L S A = 4 * (1/2) * a * l = 2 * 2 * 5.099 = 20.396#

#color(brown)(T S A = A_b + L S A = 3,464 + 20.396 = 23.86 " sq units"#