An example.... one file in geographic and one in projected coordinates...
in_fc = r"C:\....\arcpytools_demo.gdb\Can_0_big_3"
desc = arcpy.Describe(in_fc)
ext = desc.extent
ext.spatialReference.name
'GCS_WGS_1984'
in_fc2 = r"C:\Git_Dan\a_Data\testdata.gdb\polygon"
desc2 = arcpy.Describe(in_fc2)
ext2 = desc2.extent
ext2.spatialReference.name
'NAD_1983_CSRS_MTM_9'
ext.spatialReference.name
ext.lowerLeft
<Point (-141.00686645507812, 41.67692565917997,
ext.upperRight
<Point (-52.61888885498041, 83.11042022705101,
ext2.spatialReference.name
ext2.lowerLeft
<Point (300000.0, 5000000.0,
ext2.upperRight
<Point (300020.0, 5000020.0,
ext.contains(ext2)
True
ext2.contains(ext)
False
ext.overlaps(ext2)
False
ext.within(ext2)
False
ext2.within(ext)
True
dir(ext)
['JSON', 'MMax', 'MMin', 'XMax', 'XMin', 'YMax', 'YMin', 'ZMax', 'ZMin',.... snip...
', 'contains', 'crosses', 'depth', 'disjoint', 'equals', 'geohash', 'geohashCovers',
'geohashNeighbors', 'height', 'lowerLeft', 'lowerRight', 'overlaps', 'polygon',
'projectAs', 'spatialReference', 'touches', 'upperLeft', 'upperRight', 'width',
'within']