Chapter 12.2, Problem 3CE

To determine

To find: The value of the slant height $l$ from the given figure.

Answer to Problem 3CE

The value of $l=10.$

Explanation of Solution

Given information:

V-ABCD is a regular square pyramid.

  

Calculation:

Since, the pyramid has a square base ABCD .

Calculate the measure of $OM$ from the figure.

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

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

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

Further simplify.

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

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

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