We have obtained metallicities from near-infrared calcium triplet spectroscopy for nearly a thousand red giants in 28 fields spanning a range of radial distances from the center of the bar to near the tidal radius. We have used these data to investigate the radius-metallicity and age-metallicity relations. A powerful application of these data is in conjunction with the analysis of deep HST color–magnitude diagrams (CMDs). Most of the power in determining a robust star-formation history from a CMD comes from the main-sequence turnoff and subgiant branches. The age-metallicity degeneracy that results is largely broken by the red giant branch color, but theoretical model RGB colors remain uncertain. By incorporating the observed metallicity distribution function into the modelling process, a star-formation history with massively increased precision and accuracy can be derived. We incorporate the observed metallicity distribution of the LMC bar into a maximum-likelihood analysis of the bar CMD, and present a new star formation history and age–metallicity relation for the bar. The bar is certainly younger than the disk as a whole, and the most reliable estimates of its age are in the 5–6 Gyr range, when the mean gas abundance of the LMC had already increased to [Fe/H] ≳ −0.6. There is no obvious metallicity gradient among the old stars in the LMC disk out to a distance of 8–10 kpc, but the bar is more metal-rich than the disk by ≈0.1–0.2 dex. This is likely to be the result of the bar's younger average age. In both disk and bar, 95% of the red giants are more metal-rich than [Fe/H] = −1.2.