We present a new study of late-type eclipsing binary stars in the Small Magellanic Cloud (SMC) undertaken with the aim of improving the distance determination to this important galaxy. A sample of 10 new detached, double-lined eclipsing binaries identified from the OGLE variable star catalogs and consisting of F- and G-type giant components has been analyzed. The absolute physical parameters of the individual components have been measured with a typical accuracy of better than 3%. All but one of the systems consist of young and intermediate population stars with masses in the range of 1.4 to 3.8M{sun}. This new sample has been combined with five SMC eclipsing binaries previously published by our team. Distances to the binary systems were calculated using a surface brightness-color calibration. The targets form an elongated structure, highly inclined to the plane of the sky. The distance difference between the nearest and most-distant system amounts to 10kpc with the line-of-sight depth reaching 7kpc. We find tentative evidence of the existence of a spherical stellar substructure (core) in the SMC coinciding with its stellar center, containing about 40% of the young and intermediate age stars in the galaxy. The radial extension of this substructure is ~1.5kpc. We derive a distance to the SMC center of DSMC=62.44{+/-}0.47(stat.){+/-}0.81(syst.)kpc corresponding to a distance modulus (m-M)SMC=18.977{+/-}0.016{+/-}0.028mag, representing an accuracy of better than 2%.