Let $T_{1}and{T}_2$ be two distinct common tangents to the ellipse $E:\frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P:y^2=12x$ . Suppose that the tangent $T_1$ touches P and E at the points $A_{1}and{A}_2$ respectively and the tangent $T_2$ touches P and E at the points $A_{4}and{A}_3$ respectively. If $\Delta$ square units is the area of the quadrilateral $A_1{A}_2{A}_3{A}_4$ then $\frac{\Delta }{4}$ is ___________