Yes, you can continue along that route if you like.

Triangles ABF and CEF are similar. ABF is CEF magnified.

The base of ABF is 5 and the base of CEF is 1.

This means that the perpendicular height of CEF is one-fifth of the perpendicular height of ABF,

since the linear measurements of ABF are 5 times those of CEF.

Hence you must divide AD or BC into 6 equal subdivisions.

Then you have the base and perpendicular height of CEF,

so you can find it's area.

Can you finish ?

OOps!!! sorry, that's ECF not BCF.

However, you then only need subtract the area of ECF from ECB which is easy.