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 \(k_{}.\)
(第十七届AIME1999 第6题)