Chapter 12, Problem 21SGR

To determine

To find the volume of the given triangular prism.

Answer to Problem 21SGR

972 cubic millimeters

Explanation of Solution

Given:

  

A rectangular prism

Height, $(h)=18$ centimeters

Right triangular base of the prism:

Height of the right angled triangle $=9$ centimeters.

Base of the right angled triangle $=12$ centimeters.

Formula used:

Volume of the prism $=Bh$

where $B$ is the base area and $h$ is the height of the prism.

Volume of a triangle $=\frac{1}{2}\times base\times height$

Calculation:

To find the area of the base, use the following formula.

Area $=\frac{1}{2}\times base\times height$

Putting the values,

  $\Rightarrow \frac{1}{2}\times 9\times 12$

  $\Rightarrow 54$ square centimeters

So, base area is equal to 54 square centimeters.

To find the volume of the prism, use the following formula.

Volume $=Bh$

Now putting the values,

  $\Rightarrow 54\times 18$

  $\Rightarrow 972$ cubic centimeters

Conclusion:

Hence, the volume of the given prism is 972 cubic centimeters.