AoPS Wiki:Problem of the Day/November 5, 2011

$BCDE$ is a square. Point $A$ is chosen outside of $BCDE$ such that angle $BAC = 120^\circ$ and $AB=AC$ . Point $F$ is chosen inside of $BCDE$ such that the triangles $ABC$ and $FCD$ are congruent. If $AF=20$ , compute the area of square $BCDE$ .