Formula for finding area of a triangle, and perpendicular height

[Xentus]

Hi, I'm new here, I have a question. How to solve the question below?

Calculate the perpendicular height of a triangle, with a base of 8 cm, used to make a prism 13 cm long, witha volume of 193.3 cm(3).
I've looked all over the internet on how to find the answer, but alas.

 

[MarkFL]

Hello, and welcome to FMH!

The Volume \(V\) of the prism will be the product of the area of triangular face of the prism and its length \(\ell\):

[MATH]V=\frac{1}{2}bh\ell[/MATH]
Solve for \(h\):

[MATH]h=\frac{2V}{b\ell}[/MATH]
We are given everything except \(h\), so plug in the given values...what do you get?

 

[Xentus]

I got 3.717

 

[MarkFL]

Let's check:

[MATH]h=\frac{2(193.3\text{ cm}^3)}{(8\text{ cm})(13\text{ cm})}\approx3.717\text{ cm}\quad\checkmark[/MATH]
Just remember to give the unit of measurement.

 

[Xentus]

Thanks!