To find the missing length \( l \) of a rectangular prism with given height \( h = 9 , \text{cm} \), width \( w = 9 , \text{cm} \), and surface area \( SA = 432 , \text{cm}^2 \), we can use the surface area formula for a rectangular prism:
\[ SA = 2lw + 2lh + 2wh \]
Plugging in the given values:
\[ 432 = 2(l \cdot 9) + 2(l \cdot 9) + 2(9 \cdot 9) \]
This simplifies to:
\[ 432 = 2(9l) + 2(9l) + 2(81) \] \[ 432 = 18l + 18l + 162 \] \[ 432 = 36l + 162 \]
Now, isolate \( l \):
\[ 432 - 162 = 36l \] \[ 270 = 36l \] \[ l = \frac{270}{36} \] \[ l = 7.5 \]
Thus, the missing length is:
\[ \boxed{7.5} , \text{cm} \]