Q7. - Geometry

Question

V- ABCD is a regular square pyramid. Find the following numerical answers.

$VC=\_\_\_$

Step-by-Step Solution

Answer

The length of VC is$\sqrt{136}\text{\hspace{0.17em}\hspace{0.17em}unit}$ .

Step 1. Given information.

The given$V-ABCD$ is a regular square pyramid.

Also$AB=12$, and$BC=12$ .

Step 2. Determine the area.

The length ofVC can be determined by using Pythagoras theorem in triangle VOC.

 

The length of OCcan be calculated as:

$\begin{array}{c}OC=\sqrt{O{M}^2+M{C}^2}\\ =\sqrt{6^2+6^2}\\ =\sqrt{36+36}\\ =6\sqrt{2}\end{array}$

Step 3. Determine the volume.

In triangle VOC, the length of VC is

 $\begin{array}{c}VC=\sqrt{O{C}^2+V{O}^2}\\ =\sqrt{{\left(6\sqrt{2}\right)}^2+8^2}\\ =\sqrt{72+64}\\ =\sqrt{136}\end{array}$

Therefore, the length of VC is equal to$\sqrt{136}$ unit.