Question

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

• A. $4c{m}^2$
• B. $6c{m}^2$
• C. $3\sqrt{3}c{m}^2$
• D. $\frac{3\sqrt{3}}{2}c{m}^2$

Answer 1

The correct option is C $3\sqrt{3}c{m}^2$

Area of the star $=$ Area of $\Delta ABC+$ Area of $\Delta EFG-$ Area of hexagon $HIJKLM$
The regular hexagon HIJKLM is made of $6$ equilateral triangle of side $1cm$.
$\therefore AB=BC=CA=EF=FG=GE=3cm$
$\therefore$ Required area $=2\times \frac{\sqrt{3}}{4}\times (3{)}^2-6\times \frac{\sqrt{3}}{4}(1{)}^2$
$=\frac{9\sqrt{3}}{2}-\frac{3\sqrt{3}}{2}=\frac{6\sqrt{3}}{2}c{m}^2$
$=3\sqrt{3}c{m}^2$