To find the volume \( V \) of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
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Calculate the base area: The base is a rectangle with dimensions \( 3 \) in and \( 4 \) in. So, the area \( A \) is:
\[ A = \text{length} \times \text{width} = 3 , \text{in} \times 4 , \text{in} = 12 , \text{in}^2 \]
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Use the height: The height (altitude) of the pyramid is \( 6 \) in.
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Calculate the volume: Substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 12 , \text{in}^2 \times 6 , \text{in} \]
\[ V = \frac{1}{3} \times 72 , \text{in}^3 \]
\[ V = 24 , \text{in}^3 \]
So, the volume of the rectangular pyramid is \( \boxed{24 , \text{in}^3} \).