We draw perpendiculars to the longer base from the ends of the shorter
base (in green), and let their lengths be h.  We have right triangles on
each side of the trapezoid.  We let x = the length of the bottom side of the
right triangle on the right side of the trapezoid.



In the right triangle on the right side, for the 60° angle,



Cross-multiply:

   <--the height of the trapezoid



Cross-multiply:

    <--the bottom side of the right triangle on the right.

Now we can put in the values for h and x:



We don't need to solve the right triangle on the left because we know that a
45-45-90 right triangle is isosceles and its two legs are the same length,
so we have this:













 m²

Edwin