What is the total surface area, in square feet, of a board that is 12 feet long, six inches wide, and two inches thick?

The key to solving this puzzle is first converting all measurements to a single unit: feet. The board is 12 feet long, but its width is six inches (or 1/2 of a foot) and its thickness is two inches (or 1/6 of a foot). A rectangular board has three pairs of identical sides. The two large faces have an area of 12 ft by 1/2 ft each, totaling 12 square feet. The two long, skinny edges are 12 ft by 1/6 ft each, which adds another 4 square feet. Finally, the two small end caps are 1/2 ft by 1/6 ft, which together contribute a final 1/6 of a square foot.

Adding the area of all six faces together (12 + 4 + 1/6) gives a total surface area of 16 1/6 square feet. This calculation is more than just a math exercise; it's essential for practical projects. If you were planning to paint or seal this board, you would need to know the total surface area to buy the correct amount of finish. Interestingly, in the real world, lumber is often sold by "nominal" dimensions. A common "2x6" board is actually closer to 1.5 by 5.5 inches. This problem