Question

These are numeric entry type questions.
An edge of a regular tetrahedron is $6 \sqrt{6}$ $cm$. The vertical height of the tetrahedron is ______$cm$.

Answer 1

Let $a$ be the edge of the regular tetrahedron.
Given: $a=6 \sqrt{6} cm$ Vertical height of the tetrahedron $=\sqrt{\frac{2}{3} a}$ $=\sqrt{\frac{2}{3}}(6 \sqrt{6})$
$=\sqrt{2}(6 \sqrt{2})$
$=12 cm$