How to Find the Diagonal Length of a Cube | Space Diagonal of a Cube, Geometry

How do we find the diagonal length of a cube? In today's video math lesson we derive the formula for the length of a cube's diagonal, also sometimes called the space diagonal or solid diagonal of a cube. A cube does have multiple diagonals, but they all have the same length! Try to prove that fact if you haven't already, it is pretty straightforward, you just need to use some triangles!

By introducing an additional line segment into our diagram, we are able to use the Pythagorean theorem on a newly created right triangle, and this is the key to the problem! Check out the full lesson for the detailed explanation.

The diagonal we are discussing in this video is sometimes called a space diagonal or a solid diagonal, which is a diagonal connecting vertices that share no common faces of the solid. By that I mean, if we look at the two endpoints of our diagonal, one endpoint is incident with three faces of the cube, the other is incident with 3 completely different faces of the cube, so they share no faces.Thus, the line segment joining them is a space diagonal.

This is in contrast to a face diagonal, which would be like the diagonal of the bottom square face which we use in the video. A face diagonal joins two vertices that are incident with a common face.


I hope you find this video helpful, and be sure to ask any questions
down in the comments!

+WRATH OF MATH+

◆ Support Wrath of Math on Patreon: patreon.com/wrathofmathlessons

Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● Facebook: facebook.com/WrathofMath
● Twitter: twitter.com/wrathofmathedu

My Music Channel: youtube.com/seanemusic