Rectangle $A B C D$ has side $A B$ of length $12 \, \text{cm}$ and side $B C$ of length $6 \, \text{cm}$. Point $S$ is the center of the rectangle, and point $F$ lies on side $C D$. Quadrilateral $B C F S$ has one-third the area of rectangle $A B C D$.

Determine the length of segment $C F$.

(E. Novotná)

![](https://cdn.mathpix.com/cropped/2024_04_17_4bbdd946fc9507df08ddg-3.jpg?height=411&width=828&top_left_y=1825&top_left_x=614)

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