The area not covered by six pointed star In a circle with radius $r$, two equi triangles overlapping each other in the form of a six pointed star touching the circumference is inscribed! What is the area that is not covered by the star?
Progress
By subtracting area of the star from area of circle , the area of the surface can be found! But how to calculate the area of the star?

Answer:
The required Area = Area of the Circle - (2*Area of the Equilateral Triangle - Area of the Hexagon that is formed by the superimposition of two equilateral trianle)
Area of the Circle $=\pi r^2$
Length of the equilateral triangle $\sqrt{3}r$
Area of the equilateral triangle then is = $\frac{3\sqrt{3}r^2}{4}$
Length of the hexagon (l) $= \frac{r}{\sqrt{3}}$
Area of the hexagon = $\frac{3\sqrt{3}l^2}{2}$
Thus Area of the hexagon = $\frac{3\sqrt{3}r^2}{6}$
The required area of the part of the circle uncovered by the six sided star = $(\pi r^2 - (2*\frac{3\sqrt{3}r^2}{4} - \frac{3\sqrt{3}r^2}{6}))$
which reduces to $$ = r^{2}(\pi -\sqrt{3})$$
