Chapter 12.3, Problem 19PPS

To determine

To find:

The lateral area of the pyramid.

Answer to Problem 19PPS

The lateral area of pyramid is $54846$ square yards.

Explanation of Solution

Given information:

A square pyramid measures $165$ yards on each side and the height is $20$ yards.

Calculation:

Find the slant height of the pyramid.

Apply this formula to find the slant height.

  $\begin{array}{l}{l}^2=r^2+h^2\\ l=\sqrt{r^2+h^2}\end{array}$

Substitute $r=165$ and $h=20$ in the above formula.

  $\begin{array}{c}l=\sqrt{{165}^2+{20}^2}\\ =\sqrt{27225+400}\\ =\sqrt{27625}\\ =166.20\end{array}$

So, the slant height of a cone is $166.20$ yards.

The lateral area of pyramid is $L=\frac{1}{2}Pl$ , where $l$ is the slant height and $P$ is the perimeter of the base.

Here, the base is a square of side $165$ yards and the slant height of a cone is $166.20$ yards.

  $\begin{array}{c}L=\frac{1}{2}Pl\\ =\frac{1}{2}\left(4\cdot 165\right)\left(166.20\right)\\ =2\cdot 165\left(166.20\right)\\ =330\left(166.20\right)\\ =54846\end{array}$

Hence, the lateral area of pyramid is $54846$ square yards.