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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+806 
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We can easily set up an equation to do this problem. 

 

We can do

\(\Delta EFG \cdot \frac{2h}{3}=18\\ \Delta EFG =\frac{3\cdot 18}{2h}\\ V_{EFGH}=\Delta EFG\cdot \frac{1}{3}h\\ [EFGH]=\frac{3\cdot 18}{2h}\cdot \frac{1}{3}h\\ [EFGH]=9\)

 

So 9 is our answer!

 

Thanks! :)

 Jun 8, 2024

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