Added new solution to account for limit_area with pad

provided by pandas-dev#34749

Test are green now

pandas/core/internals/blocks.py

@@ -1,4 +1,5 @@
 from datetime import datetime, timedelta
+import functools
 import inspect
 import re
 from typing import TYPE_CHECKING, Any, List, Optional
@@ -1127,6 +1128,7 @@ def interpolate(
                 axis=axis,
                 inplace=inplace,
                 limit=limit,
+                limit_area=limit_area,
                 fill_value=fill_value,
                 coerce=coerce,
                 downcast=downcast,
@@ -1155,6 +1157,7 @@ def _interpolate_with_fill(
         axis: int = 0,
         inplace: bool = False,
         limit: Optional[int] = None,
+        limit_area: Optional[str] = None,
         fill_value: Optional[Any] = None,
         coerce: bool = False,
         downcast: Optional[str] = None,
@@ -1176,15 +1179,42 @@ def _interpolate_with_fill(
         # We only get here for non-ExtensionBlock
         fill_value = convert_scalar_for_putitemlike(fill_value, self.values.dtype)
 
-        values = missing.interpolate_2d(
-            values,
+        interpolate_2d = functools.partial(
+            missing.interpolate_2d,
             method=method,
-            axis=axis,
             limit=limit,
             fill_value=fill_value,
             dtype=self.dtype,
         )
 
+        if limit_area is None:
+            values = interpolate_2d(values, axis=axis)
+        else:
+            def func(values):
+                invalid = isna(values)
+
+                if not invalid.any():
+                    return values
+
+                if not invalid.all():
+                    first = missing.find_valid_index(values, "first")
+                    last = missing.find_valid_index(values, "last")
+
+                    values = interpolate_2d(values)
+
+                    if limit_area == "inside":
+                        invalid[first : last + 1] = False
+                    elif limit_area == "outside":
+                        invalid[:first] = False
+                        invalid[last + 1 :] = False
+
+                    values[invalid] = np.nan
+                else:
+                    values = interpolate_2d(values)
+                return values
+
+            values = np.apply_along_axis(func, axis, values)
+
         blocks = [self.make_block_same_class(values, ndim=self.ndim)]
         return self._maybe_downcast(blocks, downcast)