Question

Two cardboard pieces in the form of equilateral triangles having a side of 3 cm each are symmetrically glued to form a regular star. The area of the star is

(a) 4 cm² 

(b) 6 cm² 

(c) 3√3 cm² 

(d) \(\frac{3\sqrt3}{2}\) cm² 

Answer 1

(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