O is the outer center (weight, inner center and vertical center) of positive △ABC,

A, O, M three-point * * * line,

△SOM is RT△,

According to Pythagorean theorem,

OM=√3a，

According to the nature of the center of gravity,

OM=AM/3，

∴AM=3√3a，

BM=√3AM/3=3a，

∴BC=2BM=6a，

∴S△SBC=SM*BC/2=2a*6a/2=6a^2，

∴ lateral area: s side = 3 * 6A 2 = 18A 2.

S△ABC=BC*AM/2=6a*3√3a/2=9√3a^2，

∴vs-abc=s△abc*so/3=9√3a^2*a/3=3√3a^3.