Area of the yellow region - 2

The area of the yellow region is equal to the area of the regular decagon plus the sum of the areas of the five circular sectors outside the decagon minus the sum of the areas of the five circular sectors inside the decagon.

Area of the regular decagon:

By cosine law, we have

$5^2=2x^2-2x^2\cos 36$ $\implies$ $25=x^2(2-2\cos 36)$ $\implies$ $x^2=\dfrac{25}{2-2\cos 36}$

$\text{Area} = 10\left(\dfrac{1}{2}\right)(x^2)(\sin 36)=5\left(\dfrac{25}{2-2\cos 36}\right)(\sin 36) \approx 192.355$

Area of the five circular sectors outside the decagon:

$\text{Area} = 5\left(\dfrac{216}{360}\right)(3.1416)(2.5^2)\approx 58.905$

Area of the five circular sectors inside the decagon:

$\text{Area} = 5\left(\dfrac{144}{360}\right)(3.1416)(2.5^2)\approx 39.27$

Area of the yellow region:

$\text{Area of yellow region} = 192.355+58.905-39.27 \approx 212$