+282 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 $EFGH$
+1950 This isn't too hard of a question once you realize how to do it!
ΔEFG⋅2h3=18ΔEFG=3⋅182h[EFGH]=ΔEFG⋅13h[EFGH]=3⋅182h⋅13h[EFGH]=9
The key is realizing that the pyramid is just 1/2 of EFG times the height!
Thanks! :)
