(c) \(3\sqrt3\) cm2
Area of the star = Area of ΔABC + Area of ΔEFG – Area of hexagon HIJKLM
The regular hexagon HIJKLM is made of 6 equilateral triangle of side 1cm.
AB = BC = CA = EF = FG = GE = 3 cm
∴ Required area = 2 x \(\frac{\sqrt3}{4}\times(3)^2 - 6\times\frac{\sqrt3}{4}\times(1)^2\)
= \(\frac{9\sqrt3}{2}-\)\(\frac{3\sqrt3}{2}=\) \(\frac{6\sqrt3}{2}\) cm2
= \(3\sqrt3\) cm2