In $\triangle{ADE}$, points $B$ and $C$ are on side $AD$, and points $F$ and $G$ are on side $AE$ such that $BG \parallel CF \parallel DE$. The area of $\triangle{ABG}$ is $36$, the area of trapezoid $CFED$ is $144$, and $AB = CD$. Find the area of trapezoid $BGFC$.

Let's think step by step and output the final answer within \boxed{}.
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