To find the volume of the composite figure, we will need to calculate the volumes of the rectangular prism and the two triangular prisms separately, then sum them together.
Volume of the Rectangular Prism:
The volume \( V \) of a rectangular prism is calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = 14 cm
- Width = 5 cm
- Height = 4 cm
Substituting the values:
\[ V_{\text{rectangular}} = 14 , \text{cm} \times 5 , \text{cm} \times 4 , \text{cm} = 280 , \text{cm}^3 \]
Volume of One Triangular Prism:
The volume \( V \) of a triangular prism is calculated using the formula:
\[ V = \frac{1}{2} \times \text{base} \times \text{height} \times \text{length} \]
For each triangular prism, we need:
- Base = width of the rectangular prism = 5 cm
- Height (the distance from the apex to the base) = 6 cm
- Length = length of the rectangular prism = 14 cm
Substituting the values:
\[ V_{\text{triangular}} = \frac{1}{2} \times 5 , \text{cm} \times 6 , \text{cm} \times 14 , \text{cm} \]
Calculating:
\[ V_{\text{triangular}} = \frac{1}{2} \times 5 \times 6 \times 14 = \frac{1}{2} \times 420 = 210 , \text{cm}^3 \]
Volume of Two Triangular Prisms:
Since there are two identical triangular prisms:
\[ V_{\text{2 triangular prisms}} = 2 \times V_{\text{triangular}} = 2 \times 210 , \text{cm}^3 = 420 , \text{cm}^3 \]
Total Volume of the Composite Figure:
Now, we sum the volume of the rectangular prism and the volumes of the two triangular prisms:
\[ V_{\text{total}} = V_{\text{rectangular}} + V_{\text{2 triangular prisms}} = 280 , \text{cm}^3 + 420 , \text{cm}^3 = 700 , \text{cm}^3 \]
Conclusion:
The response options provided do not match our calculated total. Let's analyze the calculations again, but based on the provided information and typical calculations for geometrical volumes, none of the response answers look correct as they are:
- 154 cm³
- 952 cm³
- 616 cm³
- 448 cm³
If my calculations hold true, which they appear to do based on the definitions and formulas used, the derived total volume of the composite figure is 700 cm³. Please recheck or clarify if there are any discrepancies in the given dimensions or in the understanding of the figure itself.