Q10. - Geometry

Question

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.

$h=\_\_\_$

Step-by-Step Solution

Answer

The length of h is$2\sqrt{6}\text{\hspace{0.17em}\hspace{0.17em}unit}$ .

Step 1. Given information.

The given$V-XYZ$ pyramid:

Each edge of pyramid is equal to 6.

Step 2. Determine the value.

Consider the triangleXOV . Each edge of pyramid XYZ is equal to 6 and the length ofXO 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$2\sqrt{6}$ .