if the parallelogram was a square the area would have been 36 (and the area would have been 90. So 90 is out.

we can create 2 equal triangles and 1 rectangle in the parallelogram. where the base of the triangle is x say.

so we know area of rectangle = (6-x)(6^2-x^2)^0.5
and area of each triangle is = 0.5*(x)(6^2-x^2)^0.5

so total area = area rect+2*area of triangle
(6^2-x^2)^0.5 [6-x+x]=18
(6^2-x^2)^0.5 = 3
(6^2-x^2) = 9
27 = x^2
x=3*sqrt(3)

so angles of triangle form a 30-60-90 relationship with 60 opposite to x. So angles are either 30 or 90+60=150 hence A

The height is 3, since area = b*h ( 18=6h )

drop perpendiculars to get two triangles.
the hypotenuse is 6 and height (of parallelogram) is 3. this forms a 30-60-90 triangle.

answer is a. ( since the parallelogram forms a 150-30-150-30 angle).