Quadrilateral ABCD: Analyzing a 3x6 Shape for Square Properties

To determine if quadrilateral ABCD is a square, we need to verify if all sides are equal and if all angles are $90^\circ$.

1. Given side lengths are $AB = 3$, $BC = 6$, $CD = 3$, and $DA = 6$. Since all sides are not equal, ABCD cannot be a square.

2. Even without needing to calculate angles, we know that a square requires all four sides to be equal, which they are not. Therefore, this characteristic alone is sufficient to conclude.

Since we determined the side lengths don't match, it logically follows that ABCD is not a square.

Therefore, the solution to the problem is No.