Question

Find the following for the regular triangular pyramid.

If AM = 9 and VA = 10, find h and l.

Short answer

$h=8\text{and}l=\sqrt{73}$

Step-by-step solution

Step 1. Given information.

The figure provided in the question,

$AM=9\text{and}VA=10$

Step 2. Determine l.

Since$AM=9$ ,

$\begin{array}{c}\frac{\sqrt{3}}{2}a=9\\ a=\frac{18}{\sqrt{3}}\text{[multiply]}\\ a=6\sqrt{3}\text{[simplify]}\end{array}$

Now,$VA=10$ ,

$\begin{array}{c}l=\sqrt{{\left(10\right)}^2-{\left(\frac{6\sqrt{3}}{2}\right)}^2}\\ =\sqrt{100-27}\text{[square]}\\ =\sqrt{73}\text{[subtract]}\end{array}$

Step 3. Determine h.

Now determine the height of pyramid.

$\begin{array}{c}{h}^2+{\left(3\right)}^2={\left(\sqrt{73}\right)}^2\\ h^2=73-9\text{[sqaureandsubtract]}\\ h^2=64\text{[subtract]}\\ h=8\text{[squareroot]}\end{array}$