Question

an oblique prism with a square base of edge length x units has a volume of $\frac{1}{2}x^3$ cubic units. which expression represents the height of the prism?
○ x units
○ $\frac{1}{2}x$ units
○ 2x units
○ $xsqrt{2}$ units

Explanation:

Step1: Recall prism volume formula

Volume $V = B \times h$, where $B$ is base area, $h$ is height.

Step2: Calculate square base area

Base edge = $x$, so $B = x \times x = x^2$.

Step3: Solve for height $h$

Substitute $V=\frac{1}{2}x^3$ and $B=x^2$ into $V=Bh$:
$$h = \frac{V}{B} = \frac{\frac{1}{2}x^3}{x^2}$$
Simplify: $h = \frac{1}{2}x$

Answer:

$\boldsymbol{\frac{1}{2}x}$ units (the second option)