Breaking A Trapezium Apart

Geometry Level 2

In the figure above, $AB$ is parallel to $CD$ . If $AB =4 \text{ cm}$ and $AD=2 \text{ cm}$ , angles $D$ and $C$ are $30^\circ$ and $60^\circ$ respectively. Find the area of the figure (in $\text{cm}^2$ ).

Give your answer to 3 decimal places.