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 $EFGH$
Find the volume of pyramid EFGH.
Hello Vxrtate!
\(\Delta EFG \cdot \frac{2h}{3}=18\\ \Delta EFG =\frac{3\cdot 18}{2h}\\ V_{EFGH}=\Delta EFG\cdot \frac{1}{3}h\\ V_{EFGH}=\frac{3\cdot 18}{2h}\cdot \frac{1}{3}h\\ \color{blue}V_{EFGH}=9\)
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