To calculate the area of the square, we either know the side length or the both the area of the triangle and its sub triangles.

1) Only one angle given; nothing can be said about the properties of the triangle. None of the quantities stated above can be determined. Insufficient. \(\Large{\color{red}\times}\)

2) Only area of large triangle is given but no area of sub triangles. Insufficient. \(\Large{\color{red}\times}\)

Taken together, both (1) and (2) remain insufficient. \(\Large{\color{red}\times}\)

Therefore, __E__ \(\Large{\color{green}\checkmark}\)

$$Statement\ 1=>\ \angle DAG=60^0$$
We are only provided with an angle. We do not have the length of any sides and we cannot calculate the area of the square without knowing the length and breadth of the square. Hence, statement 1 is NOT SUFFICIENT.

$$Statement\ 2=>\ Area\ of\ \ \triangle CDE=30\sqrt{3}m^2$$
This information does not tell us anything about the length, breadth or angles in triangle CDE. So, we cannot obtain the length DE of square DEFG from this information. Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together
$$Statement\ 1=>\ \angle DAG=60^0$$
$$Statement\ 2=>\ Area\ of\ \ \triangle CDE=30\sqrt{3}m^2$$
None of the statement provides information about either side of square DEFG. Hence, we cannot find the area of the square.
Therefore, both statements together are NOT SUFFICIENT. Thus, option E is the answer.