Q13. - Geometry

Question

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

$\text{Slant\hspace{0.17em}\hspace{0.17em}Height}=\_\_\_$

Step-by-Step Solution

Answer

The slant height of the pyramid$V-XYZ$ is equal to$3\sqrt{3}\text{\hspace{0.17em}\hspace{0.17em}cm}$ .

Step 1. Given information.

The given$V-XYZ$ pyramid:

Each edge of pyramid is equal to 6.

Step 2. Determine the slant height.

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 $3\sqrt{3}$cm.