To calculate the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area of the rectangular pyramid can be calculated by multiplying the length and the width of the base:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Now we can substitute the known values into the volume formula. We know that the volume \( V \) is 231 cubic centimeters:
\[ 231 = \frac{1}{3} \times 63 \times \text{Height} \]
To isolate the height, we can first multiply both sides by 3:
\[ 3 \times 231 = 63 \times \text{Height} \]
Calculating \( 3 \times 231 \):
\[ 693 = 63 \times \text{Height} \]
Next, we divide both sides by 63 to solve for the height:
\[ \text{Height} = \frac{693}{63} \]
Carrying out the division:
\[ \text{Height} = 11 , \text{cm} \]
Therefore, the height of the pyramid is
\[ \boxed{11 , \text{cm}} \]
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