How to find the diagonal of a tetrahedron - Advanced Geometry

Card 0 of 3

Question

Given a regular tetrahedron with an edge of $\small 10 cm$ , what is the height (or diagonal)? The height is the line drawn from one vertex perpendicular to the opposite face.

Answer

The height of a regular tetrahedron can be derived from the formula

$\small h= \sqrt{\frac{2}{3}}a$ where $\small a$ is the length of one edge.

Therefore, plugging in the side length of ,

$h=\sqrt\frac{2}{3}\cdot 10$ .

Compare your answer with the correct one above

Question

Given a regular tetrahedron with an edge of $\small \small 20 cm$ , what is the height (or diagonal)? The height is the line drawn from one vertex perpendicular to the opposite face.

Answer

The height of a regular tetrahedron can be derived from the formula $\small h= \sqrt{\frac{2}{3}}a$ where $\small a$ is the length of one edge.

Plugging in we can solve for .

$\small h= \sqrt{\frac{2}{3}}\cdot 20$

Compare your answer with the correct one above

Question

Find the height of this regular tetrahedron:

Answer

The height of a regular tetrahedron can be found using the formula $h=\sqrt{\frac{2}{3}}\cdot s$ where s is the length of the sides.

In this case, the sides have length $2\sqrt{3}$ , so we are multiplying $\sqrt{\frac{2}{3}}\cdot 2\sqrt{3}$ .

We can simplify this by multiplying the numbers inside the radical:

$2\sqrt{\frac{2}{3}\cdot 3}$ , which simplifies to $2\sqrt{2}$ .

Compare your answer with the correct one above

Tap the card to reveal the answer