Chapter 12, Problem 39SGR

To determine

To calculate:To find how many square feet of roofing material is needed to cover the roof

Answer to Problem 39SGR

  $1980$ square feet of roofing material is needed to cover the roof

Explanation of Solution

Given information:A pyramid-shaped roof has a slant height of $18$ feet and its square base is $55$ feet wide.

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:

Given that a pyramid-shaped roof has a slant height of $18$ feet and its square base is $55$ feet wide.

Here, dimensions of pyramidas follows:

  $\begin{array}{l}s=18feet\\ b=55feet\end{array}$

Amount of roofing material required to cover the roof is equal to lateral surface area of pyramid

Lateral surface of pyramid is calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Pyramid}=2\left(18\times 55\right)\\ Lateralsurfaceare{a}_{Pyramid}=2\left(990\right)\\ Lateralsurfaceare{a}_{Pyramid}=1980f{t}^2\end{array}$

Conclusion:

Hence, $1980$ square feet ofroofing material is needed to cover the roof