SOLUTION: In the diagram below, Line BD=6 cm and Line DC=2 cm. Find the ratio of the area of the parallelogram to the area of Triangle ABC Diagram: https://imgur.com/a/mD01Rx2

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