You know the area of triangle ADC.
You know the ratio of the areas of triangles CFD and ADF.
From these two points, you can get the area of CFD.
Then you can easily find the area of triangle DCE.
Thereafter, area of triangle CFE=area of triangle DCE-area of triangle CFD.
Note that , that is
So you can use the similarity of triangles CRQ and CBD.
Now you just have to find BC, because with the similarity of the two triangles, the length of RQ will follow.
To find BC, consider the triangles APS and ABD. (look at the ratios of the lengths)
I don't have time to do the third one :/