Can area from mathematics be called plot?
No, "area" cannot be replaced by "plot" in mathematics. There are two reasons:
"Area" in mathematics refers to the specific surface within a specific boundary. Plot, in common usage, refers to an indeterminate amount (abstract and without bound) of area i.e. plot of garden bed.
"Plot" in Mathematics refers to a graph of several coordinates
So, to sum up, Plotting cannot be used in place of Area, in mathematics because it causes confusion.
Notice I keep on emphasising in mathematics. This is because, in normal usage, "area" and "plot" are sometimes interchangeable. But absolutely not in mathematics.
The terms are really not synonymous. They are similar in one sense only.
plot 3 a small piece of ground marked out for a purpose such as building or gardening : a vegetable plot.
area 1b • [with adj. ] a space allocated for a specific purpose : the dining area.
Note I said they are similar — I would not call these entries synonymous at all. I would just say this is possibly the source of your confusion.
In mathematics, a plot is
plot 4 a graph showing the relation between two variables. • a diagram, chart, or map.
This is definitely not the same thing as mathematical area.
If it could than a "plot area" would be pleonasm.
Plot, in several meanings of the word, see here, can have an area.