Set down area in covering (4)
I believe the answer is:
laid
'set down' is the definition.
(I've seen this before)
'area in covering' is the wordplay.
'area' becomes 'a' (maths abbreviation).
'in' indicates putting letters inside.
'covering' becomes 'lid' (lid is a kind of covering**).
'a' going inside 'lid' is 'LAID'.
(Other definitions for laid that I've seen before include "Wagered" , "settled" , "Deposited" , "The clutch must be" , "Placed horizontally on a surface" .)