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?

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Answer 1 · 2018-05-03T06:07:34

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

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

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

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

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

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

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

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

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

$A_L = 94.12$

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

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