> I have data about  areas in square meters. I want to show this data on the
> map as moveable rectangles (all four edges  in the same length) .

Isn't that a square?

> Which is the best way to do that ?

It's schoolbook geometry.  For a given area, find the square root,
that gives the length of your sides.
To plot it on a map, you'd need some idea of where to put it.
Maybe you know the centre : then you can calculate the length of a
half-diagonal of your square.  Then plot 4 points as a polygon at that
distance from your centre in NE SE SW NW directions, using the formula
for "Destination point given distance and bearing from start point"
formula at
http://www.movable-type.co.uk/scripts/latlong.html

Don't forget the visible distortion the map projection may cause for
large shapes.

> Is there something similar to circle's
> radius for rectangles (edge length, area  ...) ?

Don't think so

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