A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #8 # and #2 # and the pyramid's height is #9 #. If one of the base's corners has an angle of #(5pi)/12#, what is the pyramid's surface area?

1 Answer
May 3, 2018

Answer:

#color(maroon)("Total Surface Area " = color(purple)(A_T = A_B + A_L = color(crimson)(15.45 + 94.12 = 109.57#

Explanation:

https://socratic.org/questions/a-pyramid-has-a-parallelogram-shaped-base-and-a-peak-directly-above-its-center-i-95

#l = 8, b = 2, theta = (5pi)/12, h = 9#

#"To find the Total Surface Area T S A"#

#"Area of parallelogram base " A_B = l b sin theta#

#A_B = 8 * 2 * sin ((5pi)/12) = 15.45#

#S_1 = sqrt(h^2 + (b/2)^2) = sqrt(9^2 + 1^2) = 9.06#

#S_2 = sqrt(h^2 + (l/2)^2) = sqrt(9^2 + 4^2) = 10.82#

#"Lateral Surface Area " A_L = 2 * ((1/2) l * S_1 + (1/2) b * S_2#

#A_L = (cancel2 * cancel(1/2)) * (l * S_1 + b * S_2) = (8 * 9.06 + 2 * 10.82)#

#A_L = 94.12#

#"Total Surface Area " A_T = A_B + A_L = 15.45 + 94.12 = 109.57#