Question 110819
My only quibble with your excellent description is that a base is the line on the bottom, so you can't have two of them in a trapezoid. Several on-line sites call them bases so I will withdraw my quibble.
Construct a line from one end of the short parallel line perpendicular to the longer parallel line.
we have a right triangle with hyp.=10.
sin(40)=opp/10
opp=sin(40)*10
opp=6.42788
This is the altitude of the trapezoid, also.
cos(40)=adj/10
adj=cos(40)*10=7.66044
This is a portion of the larger parallel line.
There is a similar portion on the other side if a 2nd altitude is constructed at the other end of the smaller parallel line.
So, the length of the larger line is 7.66044+8+7.66044=23.32... 
A=average of the parallel lines * altitude
A=((8+23.32...)/2)*6.43...
=15.66...*6.43...
=100.7... sq units
Ed