SMO 2009 Senior Round 1 Question 10

Let $ABCD$ be a quadrilateral inscribed in a circle with diameter $AC$, and let $E$ be the foot of the perpendicular from $D$ onto $AB$, as shown. If $AD=DC$ and the area of quadrilateral $ABCD$ is $24\text{ cm}^2$, find $DE$ in cm.