A 15-foot square box of cardboard used to hold four drinking cups is shown below. Each cup is tangent to two other cups and tangent to two of the edges of the box. What is the approximate area, in square feet, of the bottom of the cardboard box that is not covered by a cup, as indicated by the shaded region?

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A 15-foot square box of cardboard used to hold four drinking cups is shown below. Each cup is tangent to two other cups and tangent to two of the edges of the box. What is the approximate area, in square feet, of the bottom of the cardboard box that is not covered by a cup, as indicated by the shaded region?

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