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answer is (3/8)*sqrt(3) , think about the angles of hexagon, they are 120 degree each. so the small right triangle at each corner of the rectangle has one angle of 30 degree and one angle of 60 degree. The whole area of rectangle is sqrt(3)/2, and the four right triagles at four corners each have sqrt(3)/32 as area. so the hexagon is sqrt(3)/2 - 4*sqrt(3)/32 =(3/8)sqrt(3)