A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of $3$ 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 · 2018-04-06T11:06:47

$"Pyramid's Total Surface Area " = 51.22 " sq units"$

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

$"Given : l = 3, b = 2, h = 9$

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

$S_2 = sqrt(h^2 + (l/2)^2) = sqrt (9^2 + 1.5^2) = 9.12$

$"Area of Pyramid base " A_b = l * b * sin theta = 3 *2 * sin ((5pi)/12) = 5.8$

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

$=> cancel2 * cancel(1/2) * (3 * 9.06 + 2 * 9.12) = 45.42$

$"Total Surface Area " T S A = L S A + A_b = 45.42 + 5.8 = 51.22$

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of 3 3 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?