Leo's Jump Rope

Leo’s jump rope is 8ft long. He uses his rope to wrap a rectangle ABCD with no remainder of the rope outside ABCD. Kyle draws a circle with center A and radius AC. Kyle’s circle and the extension of AB intersect at E; Kyle’s circle and the extension of AD intersect at F. If AE = 3. What is the area of  BDFE? (FE is an arc, not a chord.)

Road Trip

Leo is one of the fastest jump ropers in his age group. Dr. Hong plans to take him and the family to the national jump rope competition in Orlando. They are going to visit a few Southeast cities between Charlotte (NC) and Orlando (FL), such as Atlanta (GA), Charleston (SC), Columbia (SC), Greenville (SC), Jacksonville (FL), Myrtle Beach (SC), Savannah (GA), Spartanburg (SC), and Tallahassee (FL). If Dr. Hong wants to start from Charlotte, visit each city only once, and go back to Charlotte, how many miles does he have to drive on the shortest path? (Please use Google Map to find out the shortest path between two cities.)