Question

the right triangular prism has a volume of 1,152 cm³. what is the value of x, the height of the prism? 6 8 12 16 12 cm x cm 12 cm

Explanation:

Step1: Recall volume formula for triangular prism

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. The base is a right - triangle with base length $12$ cm and height $12$ cm. The area of a right - triangle is $B=\frac{1}{2}\times base\times height$. So, $B=\frac{1}{2}\times12\times12 = 72$ $cm^{2}$.

Step2: Solve for the height of the prism

We know that $V = Bh$, and $V = 1152$ $cm^{3}$, $B = 72$ $cm^{2}$. Substitute these values into the formula: $1152=72x$. Solve for $x$ by dividing both sides of the equation by 72. So, $x=\frac{1152}{72}=16$ cm.

Answer:

16