Four Right Triangles in One

Geometry Level 3

Let $ABCD$ be a quadrilateral with $AB = 25, BC = 39, CD = 60$ , and $DA = 52$ , as shown above.

If the two diagonals are perpendicular to each other, yielding 4 Pythagorean triples for the 4 right triangles, and $AC : BD = 8 : 9$ , what is the area of quadrilateral $ABCD?$