Chapter 12, Problem 12STP

To determine

To find the lateral surface area of the given square pyramid.

Answer to Problem 12STP

yy $544$ feet²

Explanation of Solution

Given:

  

Height of pyramid, 13

  $h=15$ feet

Side of base of pyramid, $a=16$ feet

Formula used:

Lateral surface area of a square pyramid $=\frac{1}{2}ps$

where $p=$ perimeter of base, $s=$ slant height of the pyramid.

Slant height $,s^2={\left(h\right)}^2+{\left(r\right)}^2\text{or}s=\sqrt{{\left(h\right)}^2+{\left(r\right)}^2}$

Calculation:

Since height of the pyramid is $h=15$ and edge of the base is $a=16$ ,

Therefore, slant height of the pyramid is given as

  $\Rightarrow {\left(15\right)}^2+{\left(8\right)}^2=s^2$

  $\begin{array}{l}\Rightarrow 225+64=s^2\\ \Rightarrow 279=s^2\\ \Rightarrow s=\sqrt{289}\\ \Rightarrow s=17\end{array}$

For the given pyramid,

Perimeter of base, $p=4a$

  $\begin{array}{l}=4\times 16\\ =64\end{array}$

Lateral surface area $=\frac{1}{2}ps$

  $\begin{array}{l}=\frac{1}{2}\times 64\times 17\\ =544\end{array}$

Conclusion:

Therefore, lateral surface area of the given pyramid is $544$ feet².