HMMT 2024 G4

Let $A B C D$ be a square, and let $\ell$ be a line passing through the midpoint of segment $\overline{A B}$ that intersects segment $\overline{B C}$. Given that the distances from $A$ and $C$ to $\ell$ are 4 and 7 , respectively, compute the area of $A B C D$.