Step 1: Understand the context.
The sentence indicates the place where he slept. The natural preposition used is "under a tree."
Step 2: Analyzing the options.
(A) under – Correct, "under a tree" is the standard usage.
(B) about – Incorrect, does not indicate position.
(C) in – Not suitable, as one does not sleep "in" a tree in this context.
(D) within – Incorrect, unnatural usage here.
Step 3: Conclusion.
The correct answer is (A) under.