Chapter 12, Problem 28SGR

To determine

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

Answer to Problem 28SGR

Lateral surface area of prism $348f{t}^2$ and total surface area of prism is $437f{t}^2$

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:

  $\begin{array}{l}h=12ft\\ a=9ft\\ b=10ft\\ c=10ft\end{array}$

Lateral surface is calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Prism}=\left(10+10+9\right)\times 12\\ Lateralsurfaceare{a}_{Prism}=29\times 12\\ Lateralsurfaceare{a}_{Prism}=348f{t}^2\end{array}$

Surface area is calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Prism}=\left[\left(10+10+9\right)\times 12\right]+2\left[\frac{1}{2}\times 8.9\times 10\right]\\ Surfaceare{a}_{Prism}=\left[29\times 12\right]+\left[8.9\times 10\right]\\ Surfaceare{a}_{Prism}=348+89\\ Surfaceare{a}_{Prism}=437f{t}^2\end{array}$

Conclusion:

Hence, Lateral surface area of prism is $348f{t}^2$ and total surface area of prism is $437f{t}^2$