IMSO 2023 Mathematics — International Short Answer Question 15

In the diagram below, ABCD is a parallelogram with perimeter 36 cm, $DF=CF$, $\angle DAB=60^\circ$, $\angle FCB=30^\circ$, $\angle DEC=90^\circ$ and $\angle DBC=90^\circ$. What is the length, in cm, of AB?