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 $8$ , and its base has a corner with an angle of $( pi)/4$ . What is the pyramid's surface area?

Question

1125 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-25T08:02:20

T S A = 174.2516

AB = BC = CD = DA = a = 8
Height OE = h = 7
OF = a/2 = 8/2 = 4
$EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(7^2+4^2) = color(red)(8.0623)$

Area of $DCE = (1/2)*a*EF = (1/2)*8*8.0623 = color(red)(32.2492)$
Lateral surface area $= 4*Delta DCE = 4*32.2492 = color(blue)(128.9968)$

$/_C = pi - (3pi)/4 = (pi)/4$
Area of base ABCD $= a* a * sin /_C = 8^2 sin (pi/4) = 45.2548$

T S A $= Lateral surface area + Base area$
T S A $=128.9968 + 45.2548 = color(purple)(174.2516)$

enter image source here

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 8 8 , and its base has a corner with an angle of ( pi)/4 ( pi)/4 . What is the pyramid's surface area?