The formula for the volume \( V \) of a pyramid is given by:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular base, the base area \( A \) is calculated as:
\[ A = \text{length} \times \text{width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Now we'll substitute the known values into the volume formula:
\[ 231 , \text{cm}^3 = \frac{1}{3} \times 63 , \text{cm}^2 \times h \]
We can multiply both sides by 3 to eliminate the fraction:
\[ 3 \times 231 = 63 \times h \]
Calculating \( 3 \times 231 \):
\[ 693 = 63h \]
Next, divide both sides by 63 to solve for \( h \):
\[ h = \frac{693}{63} = 11 , \text{cm} \]
Thus, the height of the pyramid is:
\[ \boxed{11 , \text{cm}} \]
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