hi

see diagram.

Construct midpoints L and M as shown. DL ia parallel to AB etc.

Let BED have area = 3k

Using parallel rule the following also have area 3k

FMD, BDM, MLB, MLD, ALD, AML. => LDC = 3k too.

ABC = 12k

ABD = ADC by median rule => ADC = 6k = ABD

ABF = ABD (parallel rule) => BFD = AFD

To do the rest I need to show that BF:FD = 2:1

At the moment I cannot see how to do that without using similarity so I'll post this and keep trying.

Bob