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Yes a unit for measure can be used as a tessellating shape:)
The question cannot be answered because it makes no sense. The perimeter - of a shape - is the outline of the shape. The is no unit in 20 outlines. Unless you count an outline as a unit and in that case, there are 20.
That shape is a unit equilateral triangular dipyramid, and it has 6 faces.
you do not, one is a unit of measure, the other is a shape.
The area of a shape is always the unit squared.