Walking on a Box

The box above has a width that is twice its height and a length that is twice its width.

What is the shortest walking distance along the edges of the box between opposite vertices A and B? Give your answer in terms of the height of the box.

What is the shortest walking distance on the surface of the box between opposite vertices A and B? Give your answer in terms of the height of the box.

What is the shortest “flying” distance inside the box between opposite vertices A and B? Give your answer in terms of the height of the box.

This Geometer’s Sketchpad template may be helpful: