Chapter 12, Problem 3PT

To determine

To calculate:To find the volume of a triangular prism whose base of triangle is $12$ $cm$ , altitude of triangle is $8$ $cm$ , height of prism is $4$$cm$ .

Answer to Problem 3PT

The volume of the triangular prism is $192$

  $c{m}^3$ .

Explanation of Solution

Given information:

Given triangular prism with

Base of triangle $=$ $12$ $cm$

Altitude of triangle $=$ $8$ $cm$

Height of prism $=$ $4$ $cm$

Formula Used:

Volume of a triangular prism is given by:

  $V=\frac{1}{2}\times b\times a\times h$ ; where

  $b$ is the base of triangle

  $a$ is the altitude of triangle

  $h$ is the height of prism

Calculation:

Given triangular prism with

Base of triangle $=$ $12$ $cm$

Altitude of triangle $=$ $8$ $cm$

Height of prism $=$ $4$ $cm$

Substituting the values in above equation, we have:

  $V=\frac{1}{2}\times 12\times 8\times 4$

Solving the above equation, we have:

  $V=192$

Thus, the volume of the triangular prism is $192$ $c{m}^3$ .

Conclusion:

The volume of the triangular prism is $192$ $c{m}^3$ .