Chapter 12, Problem 42SGR

To determine

To calculate:To find the surface area of new prism

Answer to Problem 42SGR

New area of prism is $10f{t}^2$

Explanation of Solution

Given information:A prism has a surface area of $160f{t}^2$ and the dimensions are reduced by a factor of $\frac{1}{4}$

Calculation:

Given a prism that has a surface area of $160f{t}^2$ and the dimensions are reduced by a factor of $\frac{1}{4}$

New surface area of prism is calculated as

  $\begin{array}{l}Area={\left(\frac{1}{4}\right)}^2\times 160\\ Area=\frac{1}{4}\times \frac{1}{4}\times 160\\ Area=\frac{1}{1}\times \frac{1}{1}\times 10\\ Area=10f{t}^2\end{array}$

Conclusion:

Hence,new area of prism is $10f{t}^2$