To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid, which is given by:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area is a rectangle with a length of 7 cm and a width of 9 cm. Therefore, the area of the base can be calculated as follows:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
We know that the volume \( V \) of the pyramid is 231 cubic centimeters. Substituting the values we have into the volume formula, we get:
\[ 231 = \frac{1}{3} \times 63 \times h \]
To isolate \( h \) (the height), we first multiply both sides of the equation by 3 to eliminate the fraction:
\[ 231 \times 3 = 63 \times h \]
Calculating the left side:
\[ 693 = 63h \]
Next, we solve for \( h \) by dividing both sides by 63:
\[ h = \frac{693}{63} \]
Now, performing the division:
\[ h = 11 \]
Thus, the height of the pyramid is 11 centimeters. In conclusion, after applying the volume formula for a rectangular pyramid and using the dimensions provided, we calculated that the height of the pyramid measures 11 cm.