If the dimensions of the space are listed in feet, you will be multiplying some quantity of feet by another. Let's say it's 7 by 9. That's actually 7 x foot x 9 x foot, which results in 63 feet squared.
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In the US it is customary to say "square" before the unit when speaking of area. So one would say square feet, square meters, square inches, and so on.
When you say an area is so many square feet, what you mean is the area you are measuring could fit 433 squares of 1 foot sides. You cannot really break this down into feet exactly as it is a mesurment of length, not area, you could argue that the length of the area measured was 221.5 feet in length and 2 feet in width Area=Length x Width so 221.5 X 2 = 433ft2), but you cannot break down square feet into feet as such. Thanks
Assuming the room is 19 ft by 13 ft (the question does not say so), the area would be 19*13 = 247 square feet
Nothing - both terms are interchangeable - and refer to the same area. You could say "The playground is 30 metres square" - OR - "The playground is 30 square metres"
You cannot convert square feet, a measure of area, into yards, a measure of length. However, you can convert feet into yards and square feet into square yards, and I am sure you would find an exact conversion chart on the internet easily.