Question 823877
Since the problem does not state any side measurements (just a ratio), the most that we could do is calculate that sum of areas relative to the area of the parallelogram.
Without a picture, I am not quite sure I can interpret the situation intended, but I will try.
 
We could calculate that sum of areas as {{{(1/2)*area}}}{{{of}}}{{{ABCD}}} for the situation below.
{{{drawing(300,200,-1,14,-1,9,
line(0,0,3,8),line(13,8,3,8),
line(0,0,10,0),line(13,8,10,0),
arrow(0,0,4,0),arrow(3,8,7,8),
arrow(0,0,1.5,4),arrow(10,0,11.5,4),
locate(-.2,0,A),locate(2.8,8.8,B),
locate(9.8,0,D),locate(13,8.8,C),
locate(4.8,0,b),locate(7.8,8,b),locate(8.8,4.4,h),
arrow(9,5,9,8),arrow(9,3,9,0),
green(line(-1,6,14,6)),green(arrow(10,6,10,8)),
green(arrow(10,8,10,6)),locate(10.1,8,green(h/4)),
red(circle(2.25,6,0.15)),locate(2.25,6,E)
)}}} 
In that case, {{{BE=(1/3)AE}}} ,
{{{area}}}{{{of}}}{{{BCE=(1/2)b*(h/4)}}}
{{{area}}}{{{of}}}{{{ADE=(1/2)b*(3h/4)}}}
{{{area}}}{{{of}}}{{{ABCD=b*h}}}
area of ADE + area of BCE ={{{(1/2)b*(3h/4)+(1/2)b*(h/4)}}}
area of ADE + area of BCE ={{{(1/2)b*(3h/4+h/4)}}}
area of ADE + area of BCE ={{{(1/2)b*h)}}}
It really does not matter what fraction of AE is BE,
because the heights of ADE and BCE would add up to {{{h}}} anyway.


It really does not matter where E is located, as long as it is between the lines AD and BC,
{{{drawing(300,200,-1,14,-0.8,9.2,
line(0,0,3,8),line(13,8,3,8),
line(0,0,10,0),line(13,8,10,0),
arrow(0,0,4,0),arrow(3,8,7,8),
arrow(0,0,1.5,4),arrow(10,0,11.5,4),
locate(-.2,0,A),locate(2.8,8.8,B),
locate(9.8,0,D),locate(12.9,8.8,C),
locate(4.8,0,b),locate(7.8,8,b),locate(8.8,4.4,h),
arrow(9,5,9,8),arrow(9,3,9,0),
red(circle(5.8,6.9,0.1)),red(arrow(3,8,5.8,6.9)),
red(arrow(5.8,6.9,3,8)),locate(4,7.5,x),
red(arrow(2.9,3.45,5.8,6.9)),red(arrow(2.9,3.45,0,0)),
locate(3.2,4,3x),locate(5.9,7.3,E)
)}}} because we could still calculate the areas of ADE and BCE
based on {{{b}}} (the length of AD and BC) as the base for both,
and the distances from E to AB and to BC as the heights.
And those heights would add up to {{{h}}} anyway.
The ratio of AE is BE, does not matter either,
because the heights of ADE and BCE would add up to {{{h}}} anyway.