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If you are asking for the area of a shape that is 10 feet by 12 feet, the answer is 120 sq feet. length (units) x width (units) = area (sq units). Remember, the units must be the same.
Any shape can have a perimeter of 6 units, depending on what those units are.
The perimeter and area of a shape do not provide sufficient information. With a given perimeter, the largest area that you can enclose is a circle, but you can then flatten the circle to reduce its area. Similarly, in terms a of quadrilaterals, a square has the largest area, but it can be flexed into a rhombus whose area can be made as small as you like. All that can be said is that there is no shape with a perimeter of 12 units whose area is 12 square units.
There is no information as to what the underlying shape is! It is not even clear that the lines are all in the same plane!
Any closed shape, at all.