A Funky Yin Yang

The regions all have the same area! We will show this by calculating the individual area of each colored region. For the ease of calculation, let's assume that the distances are $AB = BC = CD = 2$ .

Red region: $(\pi \times 1^2) + ((\pi \times 3^2) - (\pi \times 2^2)) = 6 \pi$ .

Yellow region: $( (\pi \times 2^2) - (\pi \times 1^2) ) + ( (\pi \times 2^2) - (\pi \times 1^2) ) = 6 \pi$ .

Green region: $(( \pi \times 3^2) - (\pi \times 2^2) ) + (\pi \times 1^2) = 6 \pi$ .

Write a solution. AB =BC=CD= D/3. Rest is simple geometry and addition subtraction of areas.

Consider the total area of semi circle with diameter AD. Assume that diameter of a circle is 3units and each space of AB=BC=CD= divided equally into 1unit...the total area of semi circle with diameter AD is 9pi/8 sq. unit. Now take the area of semi region of CD we have 9pi/8 - 4pi/8 = 5pi/8 sq.unit Then take the area of semi region of BC we have 4pi/8 - pi/8=3pi/8 sq. unit Then remaining is semi circle AB =pi/8 To get the total Area of Red =pi/8 +5pi/8=6pi/8 this also equal to the area of Green Region..now lets go back to yellow region.. Since we consider the half region of BC we have to multiply it by two we got the area of 3pi/8 × 2 = 6pi/8 sq. unit therefore all region are equal..all region has an equal area of 6pi/8 sq. units therefore all region Red, Yellow and Green Region have the same equal area.

Assuming AB=BC=CD=2 and only using area = πr²

Half of Yellow = (πAC²/2) – (πAB²/2) = (π2²/2) – π1²/2) = (2π) – 1/2π) = 3/2π

So Yellow area = 3π

Entire area = πAD² = π3² = 9π

If entire area = 9π and Yellow = 3π then Red + Green = (9π - 3π) = (2 x 3)π

Red and Green have the same shape so both areas are equal. So Red = Green = 3π

So each areas are 3π meaning that all are equal.