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There are linear feet, and square feet, but no "linear square feet".
Feet can't be converted to square feet. Feet measure length, while square feet measure area.
if the board is 8 inches width by 8 foot long by 2 inches thick at $5.50 per linear board what is the price per board?
20 square feet.
Square feet measure area and linear feet measure length. If a board is one (linear) foot long, that does not tell you how much area it covers, unless you also know the width.