Coordinate Geometry: JEE Main 2025 Mathematics question

Let $ABCD$ be a trapezium whose vertices lie on the parabola $y^2 = 4x$. Let the sides $AD$ and $BC$ of the trapezium be parallel to $y$-axis. If the diagonal $AC$ is of length $\frac{25}{4}$ and it passes through the point $(1,0)$, then the area of $ABCD$ is