To find the length of the base of the parallelogram, we can use the formula for the area of a parallelogram:
\[ \text{Area} = \text{base} \times \text{height} \]
We can rearrange this formula to solve for the base:
\[ \text{base} = \frac{\text{Area}}{\text{height}} \]
Given that the area is \( 37.72 , \text{m}^2 \) and the height is \( 4.6 , \text{m} \), we substitute these values into the formula:
\[ \text{base} = \frac{37.72 , \text{m}^2}{4.6 , \text{m}} \]
Now, performing the calculation:
\[ \text{base} = \frac{37.72}{4.6} \approx 8.19 , \text{m} \]
Thus, the length of the base of the parallelogram is approximately \( \boxed{8.19} \) m.