如图1,已知正六边形ABCDEF中,阴影部分面积为12倍的根号3,则正六边形的边长为?

条件不齐备!设外接圆半径为R内接正六边形面积为S6由6个边长为R的等边三角形面积为S0组成，内接正三边形面积为S3,边长3^(1/2)R S3=3*3^(1/2)*R^2/4故S6=6*S0=6*（R*(3/4)^(1/2)*R/2)=3*3^(1/2)*R^2/2依题意S6-S3=12*2^(1/2)6*（R*(3/4)^(1/2)*R/2)=3*3^(1/2)*R^2/2-3*3^(1/2)*R^2/4= 12*2^(1/2)R=6^(1/2)内接正三边形边长3^(1/2)R =3^(1/2)*6^(1/2) =3*2^(1/2)