Q9. - Geometry

Question

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

$XO=\_\_\_$

Step-by-Step Solution

Answer

The length of XO is$2\sqrt{3}\text{\hspace{0.17em}\hspace{0.17em}unit}$ .

Step 1. Given information.

The given$V-XYZ$ pyramid:

Each edge of pyramid is equal to 6.

Step 2. Determine the value.

From the given figure it can be considered that the triangle XYZ is an equilateral triangle. Each edge of pyramid XYZ is equal to 6. Also, the length of XM is $3\sqrt{3}$.

 

It is known that the circumcentre divides the altitude in 2:1. So, the length of XO can be determined as:

$\begin{array}{c}XO=\frac{2}{3}XM\\ =\frac{2}{3}\left(3\sqrt{3}\right)\\ =2\sqrt{3}\end{array}$

 

Therefore, the length of XO is equal to$2\sqrt{3}$ .