Unusual Airspace

Prepping for a ground lesson today. I’d assigned a student to plan a cross-country originating from KAST, and noticed the Class E designations:

The semi-circular segments and piece-meal layout of the Class E airspace looked pretty odd, and I couldn’t let it go without trying to figure out why. Instrument rated pilots might already have a clue. I had to look it up to see if I was right. The answer is in AIM 3-2-6(e), and looking at the instrument approach procedures really cements that bit of learning. This ILS approach for KAST involves a 19 NM DME arc that exactly overlays the Class E extension on the VFR sectional.