  We use the VERITAS imaging air Cherenkov Telescope (IACT) array to obtain the
first measured angular diameter of $\beta$ UMa at visual wavelengths using
stellar intensity interferometry (SII) and independently constrain the
limb-darkened angular diameter. The age of the Ursa Major moving group has been
assessed from the ages of its members, including nuclear member Merak ($\beta$
UMa), an A1-type subgiant, by comparing effective temperature and luminosity
constraints to model stellar evolution tracks. Previous interferometric
limb-darkened angular-diameter measurements of $\beta$ UMa in the near-infrared
(CHARA Array, $1.149 \pm 0.014$ mas) and mid-infrared (Keck Nuller, $1.08 \pm
0.07$ mas), together with the measured parallax and bolometric flux, have
constrained the effective temperature. This paper presents current VERITAS-SII
observation and analysis procedures to derive squared visibilities from
correlation functions. We fit the resulting squared visibilities to find a
limb-darkened angular diameter of $1.07 \pm 0.04 {\rm (stat)} \pm 0.05$ (sys)
mas, using synthetic visibilities from a stellar atmosphere model that provides
a good match to the spectrum of $\beta$ UMa in the optical wave band. The
VERITAS-SII limb-darkened angular diameter yields an effective temperature of
$9700\pm200\pm 200$ K, consistent with ultraviolet spectrophotometry, and an
age of $390\pm 29 \pm 32 $ Myr, using MESA Isochrones and Stellar Tracks
(MIST). This age is consistent with $408 \pm 6$ Myr from the CHARA Array
angular diameter.
