Can either use:
Clipper
Put the larger areas as the Clippee, and the area layer containing the triangle as the Clipper. Anything on the Outside Port are the parts of the polygons that are not within the triangular area.
AreaOnAreaOverlayer with List Output Mode turned On
This creates a Union of the 2 polygon layers, with a List of the attributes of the source polygons. Any output area that has list attributes from both layers overlay, whereas if the list only contains attributes from one of the layers then they don't overlay.
Send the output of AreaOnAreaOverLayer to ListSearcher, and Search the index for an Attribute Value or Attribute Name that only occurs in the Triangle Area polygons. Anything on the "Not Found" Port are the sub-areas that are the difference between the two layers.
If the areas are clean enough, you don't need to use Lists and can just look at the Overlap Count Attribute value instead from AreaOnAreaOverlayer, but otherwise List Searching will definitively tell you.