Question 6
A transformation of the first quadrant of the coordinate plane maps each point $(x, y)$ to the point $(\sqrt{x}, \sqrt{y}).$ The vertices of quadrilateral $ABCD$ are $A = (900, 300),$ $B = (1800, 600),$ $C = (600, 1800),$ and $D = (300, 900).$ Let $k$ be the area of the region enclosed by the image of quadrilateral $ABCD.$ Find the greatest integer that does not exceed $k.$