In square ABCE, AF=2FE and CD=2DE. What is the ratio of the area of △BFD to the area of square ABCE?
[asy]
size((100));
draw((0,0)--(9,0)--(9,9)--(0,9)--cycle);
draw((3,0)--(9,9)--(0,3)--cycle);
dot((3,0));
dot((0,3));
dot((9,9));
dot((0,0));
dot((9,0));
dot((0,9));
label("A", (0,9), NW);
label("B", (9,9), NE);
label("C", (9,0), SE);
label("D", (3,0), S);
label("E", (0,0), SW);
label("F", (0,3), W);
[/asy]
<spanclass=′latex−bold′>(A)</span>61<spanclass=′latex−bold′>(B)</span>92<spanclass=′latex−bold′>(C)</span>185<spanclass=′latex−bold′>(D)</span>31<spanclass=′latex−bold′>(E)</span>207