The easiest way to do this (outside of using a contractor's calculator that does conversion for you) is convert the feet and inches to decimal feet. 14 and 7 / 12 is the same as 14.583 feet. Multiply 14.583 x 12 to get 175 square feet.
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215.3 square feet for this room.
To the nearest 12 inches it is 12 inches long. To the nearest 14 or 18 inches, it is 0 inches long.
6' x 12" = 72" scale = 1:72
The area of the room is 370 sq ft = 370*12*12 sq inches So number of tiles required = 370*12*12/(14*14) = 271.84 that is 272 tiles would be required. However, that answer is good only for a mathematical exercise. In real life, you will not be able to use up all the off-cuts; there will be some breakages etc. So you should allow at least 5% more tiles.