Small Muslim province of the medieval Ethiopian Empire's southern frontier, bordered by Hadiya, Dawaro and Bale; predominantly Muslim in faith and similar to its neighbors in customs and economy, likely subjugated in the same early-14th-century Amda Seyon campaigns that brought Dawaro and Hadiya to heel.
Displaced or absorbed during the Oromo migrations of the mid-16th century, alongside the neighboring Hadiya, Dawaro and Bale provinces; its precise territory is contested in scholarship (local Oromo/Hadiya oral tradition identifies it with 'Shirk' in eastern Arsiland).
The atlas holds 4 border frames for Sharkha — the shape you scrub through changes in 1200 · 1317 · 1515 · 1533.
The scholarly source Wikipedia itself cites for what little is known of Sharkha's borders and identity (Open Library-verified).