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In a certain regular square pyramid, all of the edges have length $12$. Find the volume of the pyramid.

 Apr 11, 2022
 #1
avatar+36433 
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Find the height of the pyramid     to be sqrt 108         (use pythag theorem)

 

volume = 1/3 (12)(12) (sqrt(108))    units3

 Apr 11, 2022
 #2
avatar+124592 
+1

sqrt (3) / 2  =   slant height  / 12

 

6sqrt (3) =  sqrt (108) = slant height

 

Height    = sqrt (108 - 36)  =  sqrt (72) = 6sqrt (2)

 

Volume   = 

 

(1/3) 12^2 * 6 sqrt (2)  = 

 

288 sqrt (2) units^3

 

 

cool cool cool

 Apr 11, 2022

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