Chapter 12.2, Problem 10CE

To determine

To find: The numerical value of $h$ .

Answer to Problem 10CE

The height $h$ is equal to $2\sqrt{6}$ .

Explanation of Solution

Given information: The given figure is as follows.

  

Calculation:

Consider the triangle $XOV$ . Each edge of pyramid $XYZ$ is equal to $6$ and the length of $XO$ is equal to $2\sqrt{3}$ .

In triangle $XOV$ , use Pythagoras theorem to find the height $h$ as:

  $\begin{array}{c}h=\sqrt{X{V}^2-X{O}^2}\\ =\sqrt{6^2-{\left(2\sqrt{3}\right)}^2}\\ =\sqrt{36-12}\\ =2\sqrt{6}\end{array}$

Therefore, the height $h$ is equal to $2\sqrt{6}$ .