Question

the volume of this triangular prism is 1,080 cubic meters. what is the value of z? 18 m 10 m z = meters

Explanation:

Step1: Recall volume formula

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height. The base is a triangle with base $z$ and height $18$ m, so $B=\frac{1}{2}\times z\times18 = 9z$, and the height of the prism $h = 10$ m.

Step2: Set up the equation

We know $V = 1080$ cubic - meters. Substitute into the formula: $V=Bh$ gives $1080=9z\times10$.

Step3: Simplify the equation

$9z\times10 = 90z$, so the equation becomes $90z = 1080$.

Step4: Solve for z

Divide both sides of the equation by 90: $z=\frac{1080}{90}=12$.

Answer:

12