Since two adjacent angles of a parallelogram are supplementary, we find
that the lower left angle is 180°-120° = 60°:



Area = base × height

We have the base, which is 15 inches, but we need the height, the
ACTUAL height, not the length of the slanted sides.  So we draw a 
perpendicular from a vertex to the opposite side.  I'll draw it
in green and label it h:



The right triangle on the left has a 60° angle, therefore it is a
30°60°90° right triangle, and therefore its shorter side (the bottom
side) is  the length of the hypotenuse, and  of 8 is
4. so the bottom side of the quadrilateral has been split into
two parts, 4 inches and 11 inches:



We now use the Pythagorean theorem to calculate the length of the
green altitude:












                                              __
Now we have the height of the parallelogram 4√3, and we know the base of
the parallelogram is 15.

Since 

Area = base × height,
               __
Area = 15 × 4√3
          __
Area = 60√3 square inches

Edwin