Step 1 :Given that the length of the box is 34 inches, the width is \(33 \frac{1}{4}\) inches, and the height is 6 feet.
Step 2 :First, we need to convert the height from feet to inches. There are 12 inches in a foot, so the height in inches is \(6 \times 12 = 72\) inches.
Step 3 :The surface area of a box (or a rectangular prism) is given by the formula \(2lw + 2lh + 2wh\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
Step 4 :Substitute the given values into the formula, we get the surface area in square inches is \(2 \times 34 \times 33.25 + 2 \times 34 \times 72 + 2 \times 33.25 \times 72 = 11945.0\) square inches.
Step 5 :Finally, we need to convert the surface area from square inches to square feet. There are 144 square inches in a square foot, so the surface area in square feet is \(11945.0 \div 144 = 83\) square feet.
Step 6 :\(\boxed{83}\) is the surface area of the box in square feet.