Question

the volume of this triangular prism is 1,530 cubic centimeters. what is the value of a? 15 cm 12 cm a a = centimeters

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 (length) of the prism. The base is a triangle with base $b = 12$ cm and height $h_{triangle}=15$ cm, so the area of the base $B=\frac{1}{2}\times12\times15$.
$B=\frac{1}{2}\times12\times15 = 90$ $cm^{2}$

Step2: Solve for $a$

We know that $V = Bh$, and $V = 1530$ $cm^{3}$, $B = 90$ $cm^{2}$, and the length of the prism is $a$. Substituting the values into the formula $V=Bh$ gives $1530=90\times a$.
To find $a$, we use the formula $a=\frac{V}{B}$. So $a=\frac{1530}{90}=17$ cm.

Answer:

17