Chapter 12, Problem 14PT

To determine

To calculate:To find the surface area of model

Answer to Problem 14PT

The surface area of pyramid is $340i{n}^2$

Explanation of Solution

Given information:Chen is creating a model of a building, building is in shape of a pyramid with square base with sides of $10$ inches and a slant height of $12$ inches

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 abuilding in shape of a pyramid with square base with sides of $10$ inches and a slant height of $12$ inches

Here, dimensions of pyramidas follows:

  $\begin{array}{l}s=12in.\\ b=10in.\end{array}$

Surface area of pyramidis calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Pyramid}=2\left(12\times 10\right)+{\left(10\right)}^2\\ Surfaceare{a}_{Pyramid}=2\left(120\right)+100\\ Surfaceare{a}_{Pyramid}=240+100\\ Surfaceare{a}_{Pyramid}=340i{n}^2\end{array}$

Conclusion:

Hence, surface area of pyramid is $340i{n}^2$

Correct option is G.