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.
Meters (about 3 feet)
The unit of mass in SI is kilogram (kg).
depends on what item you are measuring
A balance.
It depends which property you are measuring. For linear dimensions a tape measure would be best
measuring tape
Weighing balance is used to measure mass. The metric unit is kilograms.
The answer would depend on what characteristic of the drop of water you wished to measure: its mass, surface area, volume, length, shape, refractive index, and so on. In any case, the tool would be much the same as the tool used for the traditional measurement - only the units would differ/
kilometer/ odometer
metric ruler
The metric unit force of an object is N ( newton). the tool used to measure the force of an object are force gauges ,torque gauges ,force testers.
Meters (about 3 feet)
You can use a measuring tape or a laser measuring device to measure the distance to the door in metric units, such as meters or centimeters. Simply extend the measuring tool from your starting point to the door to determine the distance.
the tool used to measure a area is a tape measure
meter
The property being measured would be volume, and the metric unit used would be milliliters (ml). Graduated cylinders are commonly used to measure the volume of liquids in milliliters.
odometer