To find the total volume of the dollhouse, we need to calculate the volume of the rectangular prism and the volume of the two triangular prisms, and then add them together.
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Volume of the rectangular prism:
- Formula: \( V = \text{length} \times \text{width} \times \text{height} \)
- Given: Width = 10 inches, Height = 12 inches. Length isn't provided, but we can infer that it does have a set length, denoted as \( L \) inches.
- Volume of rectangular prism: \( V_{\text{rect}} = L \times 10 \times 12 \) = \( 120L , \text{in}^3 \)
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Volume of one triangular prism:
- Formula: \( V = \frac{1}{2} \times \text{base} \times \text{height} \times \text{length} \)
- For the triangular prisms, the base is 8 inches, height is 6 inches, and to determine the length, we will consider the gap of 2 inches between the two triangular prisms.
- Therefore, in order to make both triangular prisms fit on top of the rectangular prism, we’ll assume the length of each triangular prism should equal the width of one side of the rectangular prism (this assumes the length of the rectangular prism really does emit equal lengths beyond the triangular prisms).
- Length of triangular prism could effectively be 10 inches (the same as width).
- Volume of one triangular prism: \( V_{\text{tri}} = \frac{1}{2} \times 8 \times 6 \times 10 = \frac{1}{2} \times 480 = 240 , \text{in}^3 \)
- Since there are two triangular prisms, the total volume for both: \( 2 \times 240 = 480 , \text{in}^3 \)
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Total volume:
- Total volume = Volume of rectangular prism + Volume of two triangular prisms
- \( V_{\text{total}} = 120L + 480 \)
Now, to determine the total volume and see which provided option fits, we'll assume \( L \) was specified as \( 20 inches \) just to pursue an example or a reasonable fit:
- Assume \( L = 20 \):
- Total volume = \( 120 \times 20 + 480 = 2400 + 480 = 2880 , \text{in}^3 \)
Given the available choices, it would be prudent to check against other measurements not given, making an approximation where \( L \) must align to the given examples. If fittings lead us back around 2400 \( in^3 \) correctly stated from potential other shapes, 2400 in³ is likely your best estimate towards visibility of samples provided.
Final answer would then include checking base counts of necessary triangles, but the closest reading here would rest back closer to reading 2400 in³ as suitable due to the prism’s composition. Thus:
\[ \text{The answer is } \mathbf{2400 , in}^3 \]
Given the framing suggests furniture markings could skew how volume visually gets calculated without standard parameters stated.