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

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Answer 1 · 2018-01-31T11:48:58

Total Surface Area of Pyramid $T S A = color(purple)(42.7008)$

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Area of rhombic base

$A_r = a * a sin theta = 4^2 sin ((2pi)/3) = color(green)(13.8564)$

Area of slant triangle $A_s = (1/2) a * l$

where $l = sqrt((a/2)^2 + h^2) = sqrt(2^2 + 3^2) = color(brown)(3.5056)$

Lateral Surface Area of the Pyramid

$A_l = 4 * A_s = 4 * (1/2) * 4 * 3.5056 = color(green)(28.8444)$

Total Surface Area of Pyramid
$T S A = A_r + A_l = 13.8564 + 28.8444 = color(purple)(42.7008)$

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