To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid, which is:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we need to calculate the base area. The base of the pyramid is a rectangle, so we find the area by multiplying the length and the width:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Next, we know the volume \( V \) is 231 cubic centimeters. We can plug the values we have into the volume formula and solve for the height \( h \):
\[ 231 = \frac{1}{3} \times 63 \times h \]
To eliminate the fraction, we first multiply both sides by 3:
\[ 3 \times 231 = 63 \times h \] \[ 693 = 63 \times h \]
Now we divide both sides by 63 to solve for \( h \):
\[ h = \frac{693}{63} \]
Calculating this gives us:
\[ h = 11 , \text{cm} \]
So, the height of the pyramid is 11 centimeters.