Question

determining missing
the figure below is an oblique triangular prism.
the expression below represents the volume of the
figure written in standard form. what are the missing
values?
$ax^b + cx$
$a = $
$b = $
$c = $
(figure: oblique triangular prism with labels a, b, c, d, e, f; dimensions: 2x, $x^2 + 3$, x, 2)

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangular base is \(x^{2}+3\) and the height is \(x\). So, \(A = \frac{1}{2}(x^{2}+3)x=\frac{1}{2}(x^{3}+3x)\)

Step2: Calculate the volume of the prism

The volume of a prism \(V=A\times length\). The length of the prism is \(2x\). So, \(V=\frac{1}{2}(x^{3}+3x)\times2x\)

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Comparing with \(ax^{b}+cx\), we have:

When \(a = 1\), \(b = 4\), \(c = 3\)

Answer:

\(a = 1\), \(b = 4\), \(c = 3\)