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Wrapping Geometry

Completely inspired by Katie Steckles mathematical wrapping video. http://aperiodical.com/2015/12/video-mathematical-christmas-present-wrapping/ My wife says to first fold in the long way, then the short. So the sketch is set up that way. Can you figure out how much paper you should leave at the end so that the wrapping is okay? Can you figure out how to make it perfect?