[Math] How to calculate the surface area of a cube given a diagonal

geometrysolid-geometry

I encountered this problem while practicing for a mathematics competition.

A cube has a diagonal length of 10. What is the surface area of the cube? No Calculators Allowed.

(Emphasis mine)

I'm not even sure where to start with this, so I scribbled down some numbers and solved for a square instead of a cube. Presumably, you can calculate the diagonal of a cube using the Pythagoras Theorem somehow, though I'm not sure how.

Best Answer

It is just the pythagorean theorem: enter image description here