Focusing on "volume" has its merits, as ice grows or shrinks via 3-dimensional molecules (via the physical chemistry that works in this 3-dimensional realm), but is minimally measured (mostly modeled). When the sun shines, albedo (causing or suppressing solar heat gain) is strongly affected by sea ice area (SIA), so it is a significant component of Arctic health. Finally, sea ice extent (SIE) is meaningful, partly because it is more accurately measured, and partly because the difference between SIE and SIA gives some clues as to mid-ice sheet albedo (thus melting). (Warm marginal seas will affect future ice (or lack thereof) in those areas, but doesn't much affect Central Arctic Basin (CAB) melting.)
But as this is the "freezing" thread, we note that low SIA means there is open water where there used to be ice with the resulting significant transfer of heat from this water to the atmosphere, increasing temperature and humidity, and, most likely, snowfall on nearby ice. "Warm" (less severely cold) air depresses ice volume growth, as does increased snow cover (more insulation). Thick ice (other parameters being equal) thickens much more slowly than thin ice (due to 'self-insulation', basically). (So, here we are, back to volume!)
Yup, it's all important, and crucial to our deepening understanding of Arctic sea ice!