We use the Very Energetic Radiation Imaging telescope Array System (VERITAS) imaging air Cherenkov telescope array to obtain the first measured angular diameter of β 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 (β 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 β UMa in the near-infrared (Center for High Angular Resolution Astronomy (CHARA) Array, 1.149±0.014 mas) and mid-infrared (Keck Nuller, 1.08±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±0.04 (stat)±0.05 (sys) mas, using synthetic visibilities from a stellar atmosphere model that provides a good match to the spectrum of β UMa in the optical wave band. The VERITAS-SII limb-darkened angular diameter yields an effective temperature of 9700±200±200 K, consistent with ultraviolet spectrophotometry, and an age of 390±29±32 Myr, using MESA Isochrones and Stellar Tracks. This age is consistent with 408±6 Myr from the CHARA Array angular diameter.