To find the volume of the triangular prism-shaped container, we need to use the formula for the volume of a prism, which is:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
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Identify the base of the prism: In this case, the base is a triangle. The problem gives us the width and the height of the triangle, which are the two dimensions needed to calculate the area of the triangular base.
- Width (base of the triangle) = 9 inches
- Height of the triangle = 3 inches
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Calculate the area of the triangular base:
\[ \text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 , \text{in} \times 3 , \text{in} = \frac{1}{2} \times 27 , \text{in}^2 = 13.5 , \text{in}^2 \]
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Now find the volume: With the area of the base calculated, we'll multiply it by the length of the prism to get the volume.
- Length of the prism = 12 inches
\[ \text{Volume} = \text{Base Area} \times \text{Length} = 13.5 , \text{in}^2 \times 12 , \text{in} = 162 , \text{in}^3 \]
Thus, the volume of the container is
\[ \boxed{162 , \text{cubic inches}} \]