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we know that one angle is $30^\circ$ and another is $90^\circ$ and the sum of all the angles in a triangle is $180^\circ$ so we know that the third angle = 180 - 30 - 90 = $60^\circ$ and so the triangle is a 30-60-90 degree triangle and since $\overline{CA}$= 6 then $\overline{CB} = \overline{CA} \cdot 2=12 ~ and~ \overline{AB} = \overline{CA}\sqrt{3} = 6\sqrt3$ and the area is $\frac{6\cdot6\sqrt{3}}{2}=\frac{6\cdot6\cdot\sqrt{3}}{2}=\frac{36\sqrt3}{2}=\boxed{18\sqrt3}$

so since we know that this is a 30-60-90 triangle the base is 6sqrt3 and we can find that the area is 6*6sqrt3=36sqrt3 we then fivide by 2 to get 18sqrt3

The area of the triangle is $\Huge{18\sqrt3}$