BY-MO 2018 Problem 95

The quadrilateral $ABCD$ is inscribed in the parabola $y=x^2$ . It is known that angle $BAD=90$ , the dioganal $AC$ is parallel to the axis $Ox$ and $AC$ is the bisector of the angle BAD. Find the area of the quadrilateral $ABCD$ if the length of the dioganal $BD$ is equal to $p$ .