Make AE⊥BC at point E, AF⊥CD at point F, and cross the extension line of CD.

Then < EAF = 90.

∫∠ Bad =90

∴∠DAF=∠BAE

AB = AD，∠AEB=∠F=90

∴△ABE≌△ADF

∴AE=AF,S△ABE=S△ADF

∴ Quadrilateral AECF is a square, S quadrilateral ABCD=S square AECF=24.

∴AE=2√6

∴AC=√2AE=4√3cm