Properties of Similar Figures

Let $ABC$ be a right triangle with a right angle at $C$. Two lines, one parallel to $AC$ and the other parallel to $BC$, intersect on the hypotenuse $AB$. The lines split the triangle into two triangles and a rectangle. The two triangles have areas $512$ and $32$. What is the area of the rectangle?

Source: 2011-2012 Winter Online Math Open