Ca II triplet spectroscopy has been used to derive stellar metallicities for individual stars in four Large Magellanic Cloud fields situated at galactocentric distances of 3°, 5°, 6°, and 8° to the north of the bar. Observed metallicity distributions show a well-defined peak, with a tail toward low metallicities. The mean metallicity remains constant until 6° ([Fe/H] ~ -0.5 dex), while for the outermost field, at 8°, the mean metallicity is substantially lower than in the rest of the disk ([Fe/H] ~ -0.8 dex). The combination of spectroscopy with deep CCD photometry has allowed us to break the RGB age-metallicity degeneracy and compute the ages for the objects observed spectroscopically. The obtained age-metallicity relationships (AMRs) for our four fields are statistically indistinguishable. We conclude that the lower mean metallicity in the outermost field is a consequence of it having a lower fraction of intermediate-age stars, which are more metal-rich than the older stars. The disk AMR is similar to that for clusters. However, the lack of objects with ages between 3 and 10 Gyr is not observed in the field population. Finally, we used data from the literature to derive consistently the AMR of the bar. Simple chemical evolution models have been used to reproduce the observed AMRs with the purpose of investigating which mechanism has participated in the evolution of the disk and bar. We find that while the disk AMR is well reproduced by close-box models or models with a small degree of outflow, that of the bar is only reproduced by models with combination of infall and outflow.