zerstört
destroyed
Physically broken, destroyed, or no longer functional, often because of violence or an accident.
Nach dem Erdbeben war die halbe Stadt zerstört.
After the earthquake, half the city was destroyed.

destroyed / devastated
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destroyed
Physically broken, destroyed, or no longer functional, often because of violence or an accident.
Nach dem Erdbeben war die halbe Stadt zerstört.
After the earthquake, half the city was destroyed.

'Zerstört' is the past participle of the verb 'zerstören' (to destroy) and is used as an adjective. The prefix 'zer-' points to final destruction or breaking something.
Das alte, zerstörte Gebäude soll bald abgerissen werden.
The old, destroyed building is supposed to be demolished soon.
You can recognize the meaning from context. If 'zerstört' (destroyed/devastated) refers to an object or place, physical destruction is meant. If it refers to a person, the emotional state is meant.
Das Auto war nach dem Unfall komplett zerstört.
The car was completely destroyed after the accident.
The adjective is very often intensified with adverbs to emphasize the extent of the destruction. Common combinations are 'völlig zerstört' (completely destroyed/devastated), 'komplett zerstört' (completely destroyed), or 'total zerstört' (totally destroyed/devastated).
Meine Lieblingsvase ist heruntergefallen und nun völlig zerstört.
My favorite vase fell down and is now completely destroyed.
broken / exhausted
'kaputt' and 'zerstört' can both describe that something is no longer in good condition. 'kaputt' is more general and often colloquial: a device does not work, a plate is broken, or someone is very exhausted. 'zerstört' is stronger. It often means that something has been badly damaged or destroyed by force, an accident, or a terrible event. With feelings, 'zerstört' is also very strong and means deep despair. If something simply does not work, 'kaputt' is usually enough. If the damage seems serious and final, 'zerstört' fits better.

Nach dem Brand war die Küche fast vollständig zerstört.
After the fire, the kitchen was almost completely destroyed.
Der Drucker ist kaputt, aber vielleicht kann der Techniker ihn noch reparieren.
The printer is broken, but maybe the technician can still repair it.