Is it possible to express in a calc block some basic operations with variables and non-predefined units?

For example, if you wanted to build a code block that calculates how much money costs:

a land with an Area of 300x300 m^2 at a price of 1 $/m^2.

Would it be something like this?

#+begin_src calc
  a = 300 m
  b = 300 m
  Area = a*b
  cost = 1 ($/m^2)
  A*c

#+end_src

Is it possible to work with the "$" unit?

Why A*c won't show an arithmetic result, but ~: A c ~?

Wanted result is:

#+RESULTS:
: 90 000 $

Best regards