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:

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

$$ V = B \cdot h_{\text{prism}} = \frac{3}{2}x^2 \cdot 10 = 15x^2 $$

Answer:

• (A) \(10x^3\) cubic units
• (B) \(15x^2\) cubic units (Correct answer)
• (C) \(20x^3\) cubic units
• (D) \(30x^2\) cubic units