We know line DE is parallel to line BC. Given the Area of ADE=9 and Area of CDE=6 , find the Area of ABC.

Triangles  ADE  and DCE  are under the same height....so....their areas are to each other as their bases.....so  AD /DC  =  9 / 6  =  3 / 2

So...AD   /  AC  =   3 / 5

And triangles ADE  and ABC are similar

So......the scale factor of  AC / AD  =  5/3

And the area of triangle ABC  =  [scale factor AC /AD]^2  *  area of triangle ADE =

(5/3)^2  *  9  =

 ( 25 / 9 )  *  9  =

25  =  [ ABC ]