MathDB

In the cube

ABCDEFGH

with opposite vertices

C

and

E,

J

and

I

are the midpoints of edges

\overline{FB}

and

\overline{HD},

respectively. Let

R

be the ratio of the area of the cross-section

EJCI

to the area of one of the faces of the cube. What is

R^2?

[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]

<span class='latex-bold'>(A) </span> \frac{5}{4} \qquad <span class='latex-bold'>(B) </span> \frac{4}{3} \qquad <span class='latex-bold'>(C) </span> \frac{3}{2} \qquad <span class='latex-bold'>(D) </span> \frac{25}{16} \qquad <span class='latex-bold'>(E) </span> \frac{9}{4}

Problem Statement