How to find the diagonal of a tetrahedron

Help Questions

ACT Math › How to find the diagonal of a tetrahedron

Questions 1 - 1

Calculate the diagonal of a regular tetrahedron (all of the faces are equilateral triangles) with side length .

$\large 3\sqrt{6}$

$\large 9/2$

$\large \frac{3\sqrt{3}}{2}$

$\large \frac{9\sqrt{3}}{2}$

Explanation

The diagonal of a shape is simply the length from a vertex to the center of the face or vertex opposite to it. With a regular tetrahedron, we have a face opposite to the vertex, and this basically amounts to calculating the height of our shape.

We know that the height of a tetrahedron is ${\large }s\sqrt{\frac{2}{3}}$ where s is the side length, so we can put into this formula:

${\large} 9\sqrt{2/3} = 3(3/\sqrt3)(\sqrt2) = 3\sqrt{3\cdot2} = 3\sqrt{6}$

which gives us the correct answer.

Return to subject