Draw a line perpendicular to BD from E.  Call this h.



Area of parallelogram is |CD|*h = 2h

Area of triangle BDE = (1/2)|BD|*h = 3h



Triangle BDE is similar to triangle BCA.

(Area triangle BCA) =  * (Area triangle BDE)

where  k = |BC|/|BD| = (6+2)/6 = 8/6 = 4/3

thus   = 16/9  



Putting it all together:   

(Area parallelogram)/(Area triangle BCA) = 2h / (3h * 16/9) = 3/8 

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