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If the room is rectangular, just use the formula for the area of a rectangle. In other words, multiply length x width.
6 ft 10 in x 13 ft 10 in = 82 in x 142 in = 11,644 sq in = 11,644/144 sq ft = 80.86 sq ft I think that 13 ft 10 in = 166 inches, not 142 inches, so the answer is incorrect.
20 x20 * * * * * And why not 10 ft x 40 ft? And why do you assume it is square or rectangular?
11 ft * 13 ft = 143 sq. ft, so the room has an area of 143 sq. ft
21 ft * 10 ft = 210 sq ft = 19.51 sq metres.