It depends on what you mean by size: its length, volume, surface area or even its mass.
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"Magnitude" is the size or distance. Its measure depends on the metric that is defined on the relevant space.
If you measure area by means of the metric system, you might be using square centimeters or square meters or square kilometers, depending upon the size of the area that you are measuring.
that would be the centimetre
No
You would use a tool to measure the lengths of the sides or radii of the area and then use a formula to convert the lengths into an area. The tool would depend on the size of the object and the precision required. The tool could be an electron microscope, or a ruler, or a telescope and in general there would be no difference between a tool used to measure in the metric system or the imperial system. As an example of an unusual tool to measure area... in certain types of chemistry, the chemist needs to measure the area under a peak on a graph, and the traditional way of doing that is to cut the peaks out of the graph and weigh it on an analytical balance. Assuming the paper is fairly consistent in terms of density, the ratio of the weights is the same as the ratio of the areas.