Chapter 12, Problem 35SGR

To determine

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

Answer to Problem 35SGR

Lateral surface area of pyramid is $244.8c{m}^2$ and total surface area of pyramid is $308.8c{m}^2$

Explanation of Solution

Given information:Pyramid is

  

Formula Used:

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

  

  $Lateralsurfaceare{a}_{Pyramid}=2\left(bs\right)$

  $Surfaceare{a}_{Pyramid}=2\left(bs\right)+b^2$

Calculation:

Pyramid is given as follows

  

Here, dimensions of pyramidas follows:

  $\begin{array}{l}s=15.3cm\\ b=8cm\end{array}$

Lateral surface of pyramid is calculated as follows:

  $Lateralsurfaceare{a}_{Pyramid}=2\left(bs\right)$

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Pyramid}=2\left(8\times 15.3\right)\\ Lateralsurfaceare{a}_{Pyramid}=2\left(122.4\right)\\ Lateralsurfaceare{a}_{Pyramid}=244.8c{m}^2\end{array}$

Surface area of pyramidis calculated as follows:

  $Surfaceare{a}_{Pyramid}=2\left(bs\right)+b^2$

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Pyramid}=2\left(8\times 15.3\right)+{\left(8\right)}^2\\ Surfaceare{a}_{Pyramid}=2\left(122.4\right)+64\\ Surfaceare{a}_{Pyramid}=244.8+64\\ Surfaceare{a}_{Pyramid}=308.8c{m}^2\end{array}$

Conclusion:

Hence, Lateral surface area of pyramid is $244.8c{m}^2$ and total surface area of pyramid is $308.8c{m}^2$