All of these are -zimmer

In compound words, the LAST word decides the article. Zimmer is das, so every room built with it is das too:

• das Schlafzimmer — bedroom
• das Badezimmer — bathroom
• das Kinderzimmer — children’s room
• das Arbeitszimmer — study (Arbeit + s + Zimmer)

One rule, four free articles.