Lor
2018 AMC 8
Problem 24
In the cube 
with opposite vertices 
and 
and 
are the midpoints of edges 
and 
respectively. Let 
be the ratio of the area of the cross-section 
to the area of one of the faces of the cube. What is 
![[asy] size(6cm); pair A,B,C,D,EE,F,G,H,I,J; C = (0,0); B = (-1,1); D = (2,0.5); A = B+D; G = (0,2); F = B+G; H = G+D; EE = G+B+D; I = (D+H)/2; J = (B+F)/2; filldraw(C--I--EE--J--cycle,lightgray,black); draw(C--D--H--EE--F--B--cycle); draw(G--F--G--C--G--H); draw(A--B,dashed); draw(A--EE,dashed); draw(A--D,dashed); dot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(I); dot(J); label("$A$",A,E); label("$B$",B,W); label("$C$",C,S); label("$D$",D,E); label("$E$",EE,N); label("$F$",F,W); label("$G$",G,N); label("$H$",H,E); label("$I$",I,E); label("$J$",J,W); [/asy]](https://latex.artofproblemsolving.com/a/1/d/a1d819cf8339fd4ae7e3d612b459da3b1e8cdc7b.png)
Solution
Lor
2018 AMC 8
Problem 24
In the cube with opposite vertices and and are the midpoints of edges and respectively. Let be the ratio of the area of the cross-section to the area of one of the faces of the cube. What is
Solution