There is only one tensed verb in:
He is trapped.
Since is is the present tense third-person singular indicative of to be, this sentence is in the present tense.
As for trapped, it is an adjective. You may call it a participial adjective if you’d like. But it is not a verb, and therefore it is not a past participle.
Note that English has two sorts of productive -ed suffix for making adjectives. One is used for making adjectives out of verbs, but the other is used for making adjectives out of nouns.
- A horned lark is a lark with horns, not a lark that somebody horned. Horn is a noun, not a verb.
- A beached whale is a whale that is been stranded on the beach, not one that somebody beached. Beach is a noun, not a verb.
- A berried wood is a wood with berries in it, not one that somebody berried. Berry is a noun, not a verb.
Those are all just adjectives; they have no verb that they were derived from.
In the case of trapped, it could go either way here since trap is both a noun and a verb. But it was likely derived from the verb, which makes it a participial adjective. It stopped being a verb when it stopped being used as a verb.
For it to be considered a past participle, it has to start functioning as a verb again, and it is not doing that here. Transitive verbs take objects and can be turned into passives by putting the subject trailing behind it with a by to indicate where it went. If a bear pursued Antigonus then he might exit pursued by a bear. If Blackadder punches Shakespeare’s nose, then the nose punched by Blackadder might well begin to bleed.
Those are both past participles. But neither a pursued Sicilian nor a punched Bard involves any past participles, only adjectives, even though they started out life as verbs. To be part participles, they must continue to function as verbs, and here they do not — unlike in the previous paragraph.
You cannot test whether it is a verb merely by checking whether it comes in front of the noun or is instead used predicatively. A person who attends a costume party dressed as a devil would likely come horned. You would say that they are horned. But no one horned them; they are only wearing horns. So that is still an adjective, not a verb.
If someone takes a nap, then they are rested. Rested is just an adjective. It is not a past participle — nor can it be made into one in a passive construction since rest is intransitive. Nobody rested that person, but they are still rested, and presumably a well rested person.
In contrast, if you say that they have rested, rather than that they are rested, then rested is a past participle because it is a verb again, since it is being used in the present perfect construction. But you cannot make it a passive, since you cannot rest somebody.
You can say the same about someone who is gone versus someone who has gone. If they are gone, then gone is an adjective. If they have gone, then gone is a verb. But you cannot go somebody, so it is not passive nor can it be made such, not even things gone by the wayside, since waysides cannot go anyone.