AB=BC=CD=DA=24/4=6cm
\(AH=\sqrt{6^2-5.5^2}=\dfrac{\sqrt{23}}{2}\left(cm\right)\)
=>\(AC=\sqrt{23}\left(cm\right)\)
\(S_{DCA}=\dfrac{1}{2}\cdot\sqrt{23}\cdot5,5=\dfrac{\sqrt{23}}{4}\left(cm^2\right)\)
=>\(S_{ABCD}=\dfrac{\sqrt{23}}{2}\left(cm^2\right)\)