Question

an oblique prism has trapezoidal bases and a vertical height of 10 units.
which expression represents the volume of the prism?
\\(10x^3\\) cubic units
\\(15x^2\\) cubic units
\\(20x^3\\) cubic units
\\(30x^2\\) cubic units

Explanation:

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"new_concepts": [
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<reasoning>

Calculate the area of the trapezoidal base

\[
B = \frac{1}{2} \cdot (b_1 + b_2) \cdot h_{\text{trapezoid}} = \frac{1}{2} \cdot (x + 2x) \cdot x = \frac{3}{2}x^2
\]

Calculate the volume of the oblique prism

\[
V = B \cdot h_{\text{prism}} = \frac{3}{2}x^2 \cdot 10 = 15x^2
\]
</reasoning>

<answer>
<mcq-option>(A) \(10x^3\) cubic units</mcq-option>
<mcq-correct>(B) \(15x^2\) cubic units</mcq-correct>
<mcq-option>(C) \(20x^3\) cubic units</mcq-option>
<mcq-option>(D) \(30x^2\) cubic units</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
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"Mathematics",
"Geometry",
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]
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Answer:

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</pre_analysis>

<reasoning>

Calculate the area of the trapezoidal base

\[
B = \frac{1}{2} \cdot (b_1 + b_2) \cdot h_{\text{trapezoid}} = \frac{1}{2} \cdot (x + 2x) \cdot x = \frac{3}{2}x^2
\]

Calculate the volume of the oblique prism

\[
V = B \cdot h_{\text{prism}} = \frac{3}{2}x^2 \cdot 10 = 15x^2
\]
</reasoning>

<answer>
<mcq-option>(A) \(10x^3\) cubic units</mcq-option>
<mcq-correct>(B) \(15x^2\) cubic units</mcq-correct>
<mcq-option>(C) \(20x^3\) cubic units</mcq-option>
<mcq-option>(D) \(30x^2\) cubic units</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
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