To find the volume of a rectangular pyramid, we can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we need to calculate the area of the base. In this case, the base is rectangular, and its area can be calculated as:
\[ \text{Base Area} = \text{length} \times \text{width} = 14 , \text{in.} \times 6 , \text{in.} = 84 , \text{in.}^2 \]
Next, we have the height of the pyramid, which is given as 12 inches. Now, we can substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 84 , \text{in.}^2 \times 12 , \text{in.} \]
Calculating this step-by-step:
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Multiply the base area by the height: \[ 84 \times 12 = 1,008 , \text{in.}^3 \]
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Now, divide by 3: \[ V = \frac{1,008}{3} = 336 , \text{in.}^3 \]
Thus, the volume of the rectangular pyramid is approximately \( 336 , \text{in.}^3 \).
The answer is \( \text{D. } 336 , \text{in.}^3 \).