Chapter 12, Problem 25SGR

To determine

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

Answer to Problem 25SGR

Lateral surface area of prism is $66c{m}^2$ and total surface area of prism is $99c{m}^2$

Explanation of Solution

Given information:Prism is

  

Formula Used:

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

  $Lateralsurfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)$

  $Surfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)+2\left(Width\times Length\right)$

Calculation:

Prims is given as follows

  

Here, dimensions of prism

as follows:

  $\begin{array}{l}Length=3cm\\ Width=5.5cm\\ Height=4cm\end{array}$

Lateral surface is calculated as follows:

  $Lateralsurfacearea=2\left(Length\times Height\right)+2\left(Width\times Height\right)$

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfacearea=2\left(3\times 4\right)+2\left(5.5\times 4\right)\\ Lateralsurfacearea=2\left(12\right)+2\left(22\right)\\ Lateralsurfacearea=24+44\\ Lateralsurfacearea=66c{m}^2\end{array}$

Surface area is calculated as follows:

  $Surfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)+2\left(Width\times Length\right)$

Substituting the values, volume is

  $\begin{array}{l}Surfacearea=2\left(3\times 4\right)+2\left(5.5\times 4\right)+2\left(5.5\times 3\right)\\ Surfacearea=2\left(12\right)+2\left(22\right)++2\left(16.5\right)\\ Surfacearea=24+44+33\\ Surfacearea=99c{m}^2\end{array}$

Conclusion:

Hence, Lateral surface area of prism is $66c{m}^2$ and total surface area of prism is $99c{m}^2$