To find the volume of the composite figure, we need to calculate the volume of the rectangular prism and the volumes of the two triangular prisms.
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Volume of the Rectangular Prism: The formula for the volume \( V \) of a rectangular prism is given by: \[ V = \text{length} \times \text{width} \times \text{height} \] Substituting the values:
- Length = 14 cm
- Width = 5 cm
- Height = 4 cm
\[ V_{rectangular} = 14 , \text{cm} \times 5 , \text{cm} \times 4 , \text{cm} = 280 , \text{cm}^3 \]
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Volume of One Triangular Prism: The formula for the volume \( V \) of a triangular prism is given by: \[ V = \text{Base Area} \times \text{Height} \] The base area of a triangular prism can be computed using the formula for the area of a triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base of the triangular prism is the width of the rectangular prism (5 cm), and the height of the triangle is given as 6 cm (the distance from the apex to the base).
So, \[ \text{Base Area} = \frac{1}{2} \times 5 , \text{cm} \times 6 , \text{cm} = 15 , \text{cm}^2 \] The height of the triangular prism (the distance along the length of the rectangular prism) is the same as the length of the rectangular prism (14 cm).
Therefore, the volume of one triangular prism is: \[ V_{triangular} = \text{Base Area} \times \text{Length} = 15 , \text{cm}^2 \times 14 , \text{cm} = 210 , \text{cm}^3 \]
Since there are two identical triangular prisms, the total volume for both triangular prisms is: \[ 2 \times V_{triangular} = 2 \times 210 , \text{cm}^3 = 420 , \text{cm}^3 \]
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Total Volume of the Composite Figure: Now, we can find the total volume of the composite figure by adding the volumes of the rectangular prism and the two triangular prisms: \[ V_{total} = V_{rectangular} + 2 \times V_{triangular} = 280 , \text{cm}^3 + 420 , \text{cm}^3 = 700 , \text{cm}^3 \]
The total volume of the composite figure is 700 cm³. It seems that none of the provided options match this calculation. Please double-check the properties and dimensions provided, as the composite volume calculated here is valid based on the dimensions given.