farm, field, garden, one's specialty, (kokuji)
畑 centers on a cultivated piece of land: a farm, field, or garden where crops are grown. The extended sense of one's specialty comes from the idea of a personal field of expertise.
畑 is a Japanese kokuji created by combining 火 (fire) and 田 (field), likely representing a dry field cleared by burning or a field where fire is used in cultivation.
A field 田 with a fire 火 beside it: imagine a farmer burning stubble to prepare a dry field for planting. That field is a farm or garden, and it becomes the farmer's specialty.
For はた, picture a farmer wearing a hat while working in the field: hat -> はた, and the hat shades the farmer in the sunny field.
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field (for growing wheat, fruit, vegetables, etc.); cultivated land; vegetable plot; kitchen garden; plantation
fields (of rice and other crops)
field of flowers; flower garden; flower bed
field of flowers; flower garden; flower bed
land made arable by the slash-and-burn method; swidden; slash-and-burn farming
tea plantation; tea field
wheat field; barley field; cornfield
outside one's field; out of one's line
dry field farming; dry field crop
terraced fields; terraced farm
strawberry field; strawberry patch
tobacco field; tobacco patch
cornfield; corn field; maize field
vineyard; vinery; grape plantation
rye field
The Catcher in the Rye (1951 novel by J. D. Salinger)
hillside farm; fallow ground
sales field; business field
wheat field
mountain field; mountain farmland