# How do you find the volume of a prism if the width is x, height is 2x-1 and the length if 3x+4?

Dec 20, 2014

I'm assuming here that you mean a square prism: For every prism, the volume is given by the formula:
$\text{Volume" = "Area" times "Length}$
where $\text{Area}$ is the area of the cross-section: the figure you would have if you were to slice a little piece off the prism.

In this case, the cross section is a rectangle. The area of a rectangle can be calculated by doing $\text{height" times "width}$.

So, the formula for these kind of prisms becomes:
$V o l u m e = w \cdot h \cdot l$
where $w = \text{width", h = "height}$ and $l = \text{length}$.

Entering your values into the formula:
$x \cdot \left(2 x - 1\right) \cdot \left(3 x + 4\right)$

You can bring the $x$ inside the first parentheses:
$\left(2 {x}^{2} - x\right) \cdot \left(3 x + 4\right)$
And now, you can use FOIL.
$6 {x}^{3} + 5 {x}^{2} - 4 x$

This is the volume.
I hope this is what you meant, and that it helped.