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 $7$ , its base's sides have lengths of $5$ , and its base has a corner with an angle of $(5 pi)/8$ . What is the pyramid's surface area?

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Answer 1 · 2017-12-12T12:34:39

T S A = 97.029

AB = BC = CD = DA = a = 5
Height OE = h = 7
OF = a/2 = 5/2 = 2.5
$EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(7^2+2.5^2) = color(red)(7.433)$

Area of $DCE = (1/2)*a*EF = (1/2)*5*7.433 = color(red)(18.583)$
Lateral surface area $= 4*Delta DCE = 4* 18.483 = color(blue)(73.932)$

$/_C = pi - (5pi)/8 = (3pi)/8$
Area of base ABCD $= a* a * sin /_C = 5^2 sin ((3pi)/8) = 23.097$

T S A $= Lateral surface area + Base area$
T S A $=73.932 + 23.097 = color(purple)(97.029)$

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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 7 7 , its base's sides have lengths of 5 5 , and its base has a corner with an angle of (5 pi)/8 (5 pi)/8 . What is the pyramid's surface area?