The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?
Here we are asked to find the area of the shaded part. The figure can be split into 3 semicircle i.e. a, b and c in order to find the area.
Area of the semicircle a =12×227×82 = 100.57 cm2.
The diameter of semicircles b and c is equal to the radius of the semicircle a.Therefore the area of both the semicircles will be the same.
Area of the semicircle =12×π×r2 = 12×227×42 = 25.14 cm2
The area of the shaded part = Area of semicircle a + Area of semicircle b – Area of the semicircle c = 100.57 +25.14 – 25.14 = 100.57 cm2
The area of the shaded part is 100.57 cm2.