Q3. - Geometry

Question

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

$l=\_\_\_$

Step-by-Step Solution

Answer

The length of l is$10\text{\hspace{0.17em}\hspace{0.17em}unit}$ .

Step 1. Given information.

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

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

Step 2. Determine the value.

The edge length of square base is 12 and height of pyramid is 8.

The length of $OM$can be calculated as:

$\begin{array}{c}OM=\frac{1}{2}AB\\ =\frac{1}{2}\left(12\right)\\ =6\end{array}$

 

In $\Delta VOM$, apply Pythagoras Theorem to calculate the slant height.

 

$\begin{array}{c}{\left(VO\right)}^2+{\left(OM\right)}^2={\left(VM\right)}^2\\ 8^2+6^2=l{}^2\\ l^2=64+36\\ l^2=100\end{array}$ 

Further simplify.

$\begin{array}{c}l=\sqrt{100}\\ =\pm 10\end{array}$

 

The height cannot be negative. Neglect the negative value of l.

 

Therefore, the value of the slant height l is 10 unit.