$$Statement\ 1=>\ \angle DAG=60^0$$
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.
