Chapter 12, Problem 27SGR

To determine

To calculate:To find the lateral and surface area of prism and round to the nearest tenth

Answer to Problem 27SGR

Lateral surface area of prism $143.62m^2$ and total surface area of prism is $166.42m^2$

Explanation of Solution

Given information:Prism is

  

Formula Used:

Lateral and surface area of triangular prism is given by the below formula:

  

  $Lateralsurfaceare{a}_{Prism}=BasePerimeter\times Height$

  $Surfaceare{a}_{Prism}=BasePerimeter\times Height+2\left(BaseArea\right)$

Calculation:

Prims is given as follows

  

Here, dimensions of prism as follows:

  $\begin{array}{l}h=8.6m\\ a=5.7m\\ b=7m\\ c=4m\end{array}$

Lateral surface is calculated as follows:

  $Lateralsurfaceare{a}_{Prism}=BasePerimeter\times Height$

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Prism}=\left(7+4+5.7\right)\times 8.6\\ Lateralsurfaceare{a}_{Prism}=16.7\times 8.6\\ Lateralsurfaceare{a}_{Prism}=143.62m^2\end{array}$

Surface area is calculated as follows:

  $Surfaceare{a}_{Prism}=BasePerimeter\times Height+2\left(BaseArea\right)$

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Prism}=\left[\left(7+4+5.7\right)\times 8.6\right]+2\left[\frac{1}{2}\times 4\times 5.7\right]\\ Surfaceare{a}_{Prism}=\left[16.7\times 8.6\right]+\left[4\times 5.7\right]\\ Surfaceare{a}_{Prism}=143.62+22.8\\ Surfaceare{a}_{Prism}=166.42m^2\end{array}$

Conclusion:

Hence, Lateral surface area of prism is $143.62m^2$ and total surface area of prism is $166.42m^2$