To find the volume of a right rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times B \times h \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height (altitude) of the pyramid.
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Calculate the area of the base \( B \): The base of the pyramid is a rectangle. The area \( B \) is calculated using the formula:
\[ B = \text{length} \times \text{width} \]
Substituting the given dimensions:
\[ B = 6.75 , \text{inches} \times 10.25 , \text{inches} = 69.1875 , \text{square inches} \]
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Use the height \( h \): The height of the pyramid is given as \( 22.3 , \text{inches} \).
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Substituting \( B \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \times 69.1875 \times 22.3 \]
First, calculate \( 69.1875 \times 22.3 \):
\[ 69.1875 \times 22.3 = 1545.68775 \]
Now, divide by 3:
\[ V = \frac{1545.68775}{3} \approx 515.22925 \]
Thus, the volume of the pyramid is approximately
\[ \boxed{515.23} , \text{cubic inches} \] (rounded to two decimal places).