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A trapezoidal door mat is similar in shape to a trapezoid rug. Each dimension of the door mat is 1/3 the size of the rug. Which statement is true

A. The area of the door mat is 1/6 the area of the rug

B. The area of the door mat is 1/9 the area of the rug

C. The perimeter of the door mat is 1/6 the perimeter of the rug

D. The perimeter of the door mat is 1/9 the perimeter of the rug