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If the length of each edge of regular octahedron ABCDEF is 3, then find the area of triangle ACF.

 

 Apr 22, 2022
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Because of  symmetry, the area of triangle ACF will be the same as the area of triangle EAC

 

EC  is the base  =  the diagonal of a square with a side of 3  =    3sqrt 2

 

The height of this triangle  =    sqrt   [3^2   - [(3/2)sqrt2]^2 ]  =   sqrt  [  9   - 9/2 ] = sqrt [ 9/2]  = 3 /sqrt 2

 

So.....the area of triangle  ACF =   (1/2) [3sqrt 2] [3 /sqrt 2 ] =   9/2  = 4.5 units^2  

 

 

cool cool cool

 Apr 22, 2022

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