A 7.5 ft square is a lot bigger than a 7 ½ ft octagon and it has everything to do with math.  Specifically, geometry.  Blame Pythagoras.  When we measure an octagon, we measure across the diameter from one rib end to the other. But a square is measured across one of the flat sides. 

In fact, a 7.5 ft square offers shade coverage to an area much similar to an 11 ft octagon.  Which can be proven thanks to our friend Pythagoras and his a2 + b2 = c2 theorem.  FiberBuilt’s 7 ½ ft umbrella actually measures 93”, just over 7.5 ft (or 90”).  So 932 +932 = 1322.  And 132”/12 = 11 ft.