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

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Answer 1 · 2017-12-12T13:42:31

T S A = 33.9409

AB = BC = CD = DA = a = 4
Height OE = h = 2
OF = a/2 = 4/2 = 2
$EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(2^2+2^2) = color(red)(2.8284)$

Area of $DCE = (1/2)*a*EF = (1/2)*4*2.8284 = color(red)(5.6568)$
Lateral surface area $= 4*Delta DCE = 4*5.6568 = color(blue)(22.6272)$

$/_C = (pi)/4$
Area of base ABCD $= a* a * sin /_C = 4^2 sin (pi/4) = 11.3137$

T S A $= Lateral surface area + Base area$
T S A $=22.6272 + 11.3137 = color(purple)(33.9409)$

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