Chapter 12.2, Problem 13CE

To determine

To find: The slant height of the pyramid $V-XYZ$ .

Answer to Problem 13CE

The slant height of the pyramid $V-XYZ$ is equal to $3\sqrt{3}$ .

Explanation of Solution

Given information:

Each edge of the pyramid $V-XYZ$ is equal to $6\text{cm}$ .

  

Calculation:

Use the Pythagorean Theorem in $\Delta VMZ$ for the slant height $l$ of the pyramid.

  $\begin{array}{c}{\left(VZ\right)}^2={\left(VM\right)}^2+{\left(MZ\right)}^2\\ 6^2=l^2+3^2\\ l=\sqrt{36-9}\\ l=3\sqrt{3}\end{array}$

Therefore, the slant height of the pyramid $V-XYZ$ is equal to $3\sqrt{3}$ .