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Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

 Jun 8, 2024
 #1
avatar+1946 
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We can easily set up an equation to do this problem. 

 

We can do

ΔEFG2h3=18ΔEFG=3182hVEFGH=ΔEFG13h[EFGH]=3182h13h[EFGH]=9

 

So 9 is our answer!

 

Thanks! :)

 Jun 8, 2024

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