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

Answer: 12

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