平面上 $O,A,B$三点不共线，设 $\overline{OA}=a,\overline{OB}=b$，则 $△OAB$的面积等于

A．	$\sqrt{{\left|a\right|}^2{\left|b\right|}^2-(a·b{)}^2}$	B．	$\sqrt{{\left|a\right|}^2{\left|b\right|}^2+(a·b{)}^2}$
C．	$\frac{1}{2}\sqrt{{\left|a\right|}^2{\left|b\right|}^2-(a·b{)}^2}$	D．	$\frac{1}{2}\sqrt{{\left|a\right|}^2{\left|b\right|}^2+(a·b{)}^2}$