Abnormal But Cute Polygon

what about converting the general case into a standard one :D

Then we have $\theta=90\times{4}+180\times{2} = 720 = 2 circles$ $2\times{Area(circle)} = 4\times{π}\times{r^2} = \boxed{2π = 6.28}$

As the circles have equal radius, the black sectors can be joined to make circles. A circle is completed by $360°$ so firstable calculate the sum of angles of a hexagon as follows:

$180°\times 6- 360°=\boxed{720°}$

With $720°$ can be maked to circles so black area $=2\times \pi \times 1\times1=\boxed{2\pi}$

The sum of the interior angles is $720^\circ$ . One circle is $360^\circ$ . So we need to find the area of $\dfrac{720}{360}=2$ circles. We have

$A=2(\pi)(1^2) \approx$ $\boxed{6.283185307}$

I figured that the black area could fit in to 2 black circles. From there I just found the area of one circle (1 x 1 x 3.14) and multiplied it by 2. Therefore, the answer would be 3.14 x 2: 6.28

The sum of all n-irregular angles can be determined by $(n - 2)180$ . The sum of all angles of the hexagon is $(6 - 2)180 = 4 \cdot 180 = 720$ .

So, the shaded area is $\frac { 720 }{ 360 } \cdot { 1 }^{ 2 }\pi =2\pi \approx 6.28$ .