Chapter 12.4, Problem 48STP

To determine

To find:

The height of the prism.

Answer to Problem 48STP

The height is $23$ centimeters.

Explanation of Solution

Given information:

The volume of a triangular prism is $1380$ cubic centimeters. Its base is a right triangle, with legs measuring $8$ centimeters and $15$ centimeters.

Calculation:

Area of base is:

  $A=\frac{1}{2}bh$

Substitute $b=8$ and $h=15$ in the above formula:

  $\begin{array}{c}A=\frac{1}{2}8\cdot 15\\ =4\cdot 15\\ =60\end{array}$

Assume that the height of the triangular prism is $x$ centimeters.

Volume of a triangular prism is $V=Ax$ .

Substitute $V=1380$ and $A=60$ in the above formula.

  $\begin{array}{c}1380=60x\\ x=\frac{1380}{60}\\ =23\end{array}$

Hence, the height is $23$ centimeters.