One way to picture half-arsed: someone stands up, does half of the thing, and sits back down. The gate has one coat of paint on the top half. The plan has the first step and nothing after it. Both meanings point at the same missing half — in one it is the effort that stopped early, in the other it is the thinking. The word is rude, because arse is a coarse word for the bottom, and that edge travels with both uses.
One branch
只做了一半：力氣不夠，或想得不夠
兩個意思共用同一幅畫面，差別在「少掉的那一半」是什麼。後面接 attempt、job、effort 時，少的是力氣；接 idea、plan、scheme 時，少的是思考。看搭配的名詞就能分辨。
adjective · C1
Done with very little care or effort, so the work is only partly finished and the result is poor. It can describe the job itself or the person doing it.
敷衍了事的