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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 $EFGH$

 Feb 25, 2024
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Find the volume of pyramid EFGH.

Hello Vxrtate!

 

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

 

laugh !

 Feb 25, 2024
edited by asinus  Feb 25, 2024
edited by asinus  Feb 27, 2024

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