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 #2 #, its base has sides of length #1 #, and its base has a corner with an angle of #(3 pi)/4 #. What is the pyramid's surface area?

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Answer 1 · 2018-04-30T01:50:31

#color(blue)(T S A = 0.707 + 4.12 = 4.827 " sq units"#

#"Area of Rhombus base " A_r = l^2 sin theta#

#A_r = 1^2 * sin ((3pi)/4) = 0.707#

#"Slant height of pyramid " = s = sqrt((l/2)^2 + h^2) #

#s = sqrt((1/2)^2 + 2^2) = 2.06#

#"Area of Slant Triangle " A_s = (1/2) * l * s = (1/2) * 1 * 2.06 = 1.03#

#"Lateral Surface Area " = L S A = 4 * A-s = 4 * 1.03 = 4.12#

#color(green)("Total Surface Area " = A_T = A_r + L S A#

#color(blue)(T S A = 0.707 + 4.12 = 4.827 " sq units"#