Question 464979
Quadrilateral ABED is actually a trapezoid.
Let h be the height of the rectangle, and l, its length.

Now trapezoid ABED has height h also.  One of its parallel sides, BE, has length l/2 (since BE is half of BC).  The other parallel side has length l.  Hence the area is 

{{{A = (h/2)(l + l/2) = (h/2)((3l)/2) = (3hl)/4 = 2/3}}}

==> {{{hl = 8/9}}}, and hl gives exactly the area of the rectangle ABCD.