Chapter 12.5, Problem 46SPR

To determine

Find the volume of the prism.

Answer to Problem 46SPR

  $1140f{t}^3$

Explanation of Solution

Given:

  

Formula Used:

Volume of a prism:

  $V=Bh$ , where B is the area of the base and h is the height of the prism.

Calculation:

The base of the prism is a triangle whose base is 10 ft. and the other side is 13 ft. and the height of the prism is 19 ft.

First we need to find the height of the base triangle:

  

Find the height using the Pythagoras theorem:

  

h = $\sqrt{{13}^2-5^2}=\sqrt{169-25}=\sqrt{144}=12ft$

Area of the base = B = $\frac{1}{2}(base)(height)=\frac{1}{2}(10)(12)=60f{t}^2$

Volume of the prism = $V=Bh=60(19)=1140f{t}^3$

Hence ,

The volume of the prism is $1140f{t}^3$