Chapter 12, Problem 18PT

To determine

To calculate:To find the amount of fabric used in making the tent

Answer to Problem 18PT

The amount of fabric required in making the tent is $645f{t}^2$

Explanation of Solution

Given information:Slant height of pyramid tent is $14$ feet and its square base is $15$ feet

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 aslant height of pyramid tent is $14$ feet and its square base is $15$ feet

Here, dimensions of pyramidas follows:

  $\begin{array}{l}s=14ft\\ b=15ft\end{array}$

Amount of fabric required for the tent is calculated by finding the surface area of tent/

Surface area of pyramidis calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Pyramid}=2\left(14\times 15\right)+{\left(15\right)}^2\\ Surfaceare{a}_{Pyramid}=2\left(210\right)+225\\ Surfaceare{a}_{Pyramid}=420+225\\ Surfaceare{a}_{Pyramid}=645f{t}^2\end{array}$

Conclusion:

Hence, amount of fabric required in making the tent is $645f{t}^2$