Irini
If I understand correctly, your study area is composed of strata (subareas). Your objective (I believe) is to produce estimates of density and/or abundance for each of the strata.
The software wants to know the physical size of each of the strata for the purpose of converting the estimate of density to an estimate of abundance: abundance = density x area.
The first quantity estimated is animal density. That calculation is the adjusted number of animals in the area covered by your sampling (called N_a) divided by the area sampled. The estimated density in the region you sample is assumed to be equivalent to the
density in the entire stratum (because placement of transects is assumed random).
So the value you include in your data frame is the physical size of each stratum.