We have observed and spatially resolved a set of seven A-type stars in the nearby Ursa Major moving group with the Classic, CLIMB, and PAVO beam combiners on the CHARA Array. At least four of these stars have large rotational velocities ($v sin i$ $gtrsim$ 170 $mathrm{km~s^{-1}}$) and are expected to be oblate. These interferometric measurements, the stars observed photometric energy distributions, and $v sin i$ values are used to computationally construct model oblate stars from which stellar properties (inclination, rotational velocity, and the radius and effective temperature as a function of latitude, etc.) are determined. The results are compared with MESA stellar evolution models (Paxton et al. 2011, 2013) to determine masses and ages. The value of this new technique is that it enables the estimation of the fundamental properties of rapidly rotating stars without the need to fully image the star. It can thus be applied to stars with sizes comparable to the interferometric resolution limit as opposed to those that are several times larger than the limit. Under the assumption of coevality, the spread in ages can be used as a test of both the prescription presented here and the MESA evolutionary code for rapidly rotating stars. With our validated technique, we combine these age estimates and determine the age of the moving group to be 414 $pm$ 23 Myr, which is consistent with, but much more precise than previous estimates.
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