The geometrical effect of a noncircular plasma cross-section on the loss of alpha particles induced by a toroidal field ripple is investigated theoretically and numerically by using an orbit following a Monte Carlo code. The ripple-enhanced banana drift and the critical field ripple for ergodic orbits are very sensitive to the elongation. The effect of the triangularity on these parameters is not as important as that of the elongation. The ripple-enhanced banana drift loss shows a drastic decrease with plasma ellipticity. As the banana drift loss is reduced with ellipticity, the ripple trapping begins to dominate the total loss and shows a sharp increase with ellipticity. The resulting beneficial effect of elongation on reducing ripple-enhanced losses is weakened. Two key parameters that affect the fraction of ripple-trapped loss, the nonuniformity of the elongation and the gap between the plasma surface and the first wall, have been found. The geometrical effect is very important, not only for the basic loss mechanisms but also for the global ripple losses of alpha particles in connection with the distribution of field ripple