The volume \( V \) of a square-based pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area is \( 144 , \text{cm}^2 \) and the height is \( 12 , \text{cm} \).
Substituting the values into the formula:
\[ V = \frac{1}{3} \times 144 , \text{cm}^2 \times 12 , \text{cm} \]
Calculating the product of the base area and height:
\[ 144 \times 12 = 1728 , \text{cm}^3 \]
Now, divide by 3 to find the volume:
\[ V = \frac{1728}{3} = 576 , \text{cm}^3 \]
So, the volume of the square-based pyramid is:
\[ \boxed{576 , \text{cm}^3} \]