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The center of a regular octahedron is 3 units away from every vertex. What is the surface area of the octahedron?

 
 Dec 30, 2024
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We can  find the length of any edge  as

 

sqrt ( 3^2 + ^2)  =  sqrt (18)

 

The area of one face of the octahedron  =

 

(1/2) (sqrt 18)^2  sqrt (3) / 2 =  (9/2)sqrt 3

 

So....the total surface area =  8 * (9/2) sqrt 3  =   36sqrt 3

 

cool cool cool

 Dec 31, 2024

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