+1557 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 $EFGH$
+1926 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! :)
