Question 60
Two lines pass through the point $F(0; \frac{1}{4})$ on the Cartesian plane. These lines are perpendicular to each other and intersect the parabola $y = x^2$ at the points $A$, $B$, $C$ and $D$ (these points are mentioned in the $x$-coordinate increasing order). The difference of projections of the segments $AD$ and $BC$ to the $x$-axis equals $m$.
Find the area of the quadrilateral $ABCD$.
Find the area of the quadrilateral $ABCD$.