Finding distance between vertex A to vertex B in a cube

Question

Antawn the ant is on vertex A of a cube of side length 8. He wants to travel to vertex B of the cube, where AB is a space diagonal, but he can't travel through midair; he has to walk on the faces of the cube. What is the minimal distance Antawn needs to walk to travel to B?

Answer 1

To travel the shortest distance, Antwan must travel on a straight line from vertex A to vertex B.

To do this he travels on two consecutive faces of the cube. Draw a cube an trace this line.

He travels along a hypotenuse of a triangle with sides of 8 and 16.

 

He travels (by Pythagoras) 8√5 units.