Using a cached property on a named tuple

from typing import NamedTuple
from functools import cached_property

class Rectangle(NamedTuple):
    x: int
    y: int

    @cached_property
    def area(self):
        return self.x * self.y

I thought this class definition would complain something about the __slots__ on Rectangle, but apparently the class definition is valid. It doesn't fail until too late, if/when the getter is actually accessed:

>>> rect = Rectangle(2, 3)
>>> rect.area
...
TypeError: Cannot use cached_property instance without calling __set_name__ on it.
>>> Rectangle.

Well, that's weird, but okay..

>>> Rectangle.area.__set_name__(Rectangle, "area")
>>> rect.area
...
TypeError: No '__dict__' attribute on 'Rectangle' instance to cache 'area' property.

Is there a better recipe for cached properties on named tuples? Requirements:

• It should not appear to be a real field (x, y, area = rect should not be possible)
• It should be lazy (not eagerly computed) and cached (not recomputed every time accessed)
• Wherever the storage is should not leak memory (it should be deleted when the tuple instance itself is deleted)