Question

the bases of the prism below are right triangles. the volume of the prism is 3360 units³. find the height of the prism.

Explanation:

Step1: Calculate base - area

The base is a right - triangle with legs 16 and 30. The area of a right - triangle $A=\frac{1}{2}\times base\times height$. So, $A = \frac{1}{2}\times16\times30=240$ square units.

Step2: Use volume formula

The volume formula of a prism is $V = A\times h$, where $V$ is volume, $A$ is base - area and $h$ is height. We know $V = 3360$ and $A = 240$. Rearranging the formula for $h$, we get $h=\frac{V}{A}$.

Step3: Find the height

Substitute $V = 3360$ and $A = 240$ into the formula $h=\frac{V}{A}$. So, $h=\frac{3360}{240}=14$ units.

Answer:

14