HR 8799 is an hF0 mA5 gamma Doradus, lambda Bootis, Vega-type star best known for hosting four directly imaged candidate planetary companions. Using the CHARA Array interferometer, we measure HR 8799s limb-darkened angular diameter to be 0.342 +/- 0.008 mas; this is the smallest interferometrically measured stellar diameter to date, with an error of only 2%. By combining our measurement with the stars parallax and photometry from the literature, we greatly improve upon previous estimates of its fundamental parameters, including stellar radius (1.44 +/- 0.06 R_Sun), effective temperature (7193 +/- 87 K, consistent with F0), luminosity (5.05 +/- 0.29 L_Sun), and the extent of the habitable zone (1.62 AU to 3.32 AU). These improved stellar properties permit much more precise comparisons with stellar evolutionary models, from which a mass and age can be determined, once the metallicity of the star is known. Considering the observational properties of other lambda Bootis stars and the indirect evidence for youth of HR 8799, we argue that the internal abundance, and what we refer to as the effective abundance, is most likely near-solar. Finally, using the Yonsei-Yale evolutionary models with uniformly scaled solar-like abundances, we estimate HR 8799s mass and age considering two possibilities: 1.516 +0.038/-0.024 M_Sun and 33 +7/-13 Myr if the star is contracting toward the zero age main-sequence or 1.513 +0.023/-0.024 M_Sun and 90 +381/-50 Myr if it is expanding from it. This improved estimate of HR 8799s age with realistic uncertainties provides the best constraints to date on the masses of its orbiting companions, and strongly suggests they are indeed planets. They nevertheless all appear to orbit well outside the habitable zone of this young star.
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