Question

charles begins finding the volume of a trapezoidal prism using the formula $a = \frac{1}{2}(b_1 + b_2)h$ to find the prism’s base area.

$a = \frac{1}{2}((x + 4) + (x + 2))x$
$a = \frac{1}{2}(2x + 6)x$
$a = (x + 3)x$
$a = x^2 + 3x$

which expression can be used to represent the volume of the trapezoidal prism?
$\circ\\ 2x^3 + 6x^2$
$\circ\\ x^3 + 6x^2$
$\circ\\ x^3 + 3x^2$
$\circ\\ 2x^3 + 3x^2$

Explanation:

Step1: Recall the volume formula of a prism

The volume formula of a prism is \(V = A\times h\), where \(A\) is the base - area and \(h\) is the height of the prism.

Step2: Identify the base - area and height of the trapezoidal prism

We found that the base - area \(A=x^{2}+3x\) (from the given base - area calculation), and the height of the prism \(h = 2x\) (from the figure).

Step3: Calculate the volume

Substitute \(A=x^{2}+3x\) and \(h = 2x\) into the volume formula \(V=A\times h\).

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Answer:

\(2x^{3}+6x^{2}\)