The equation for each of the red areas is as follows:(πx^2-〖π((n-1)/n)〗^2)/2
x is the radius of the whole circle, while n is the number of coloured regions within the circle.
It appears as though each of the regions take up the same amount of space. For the three colour circle, each area is worth one third of the total space. For the four colour circle, each area is then worth one quarter of the total circle. And once again, for the five colour circle, the area takes up one fifth of the total circle.
For a circle with n areas, you would work out the red area with the same equation, (πx^2-〖π((n-1)/n)〗^2)/2
Once again, x is the radius of the whole circle and n is the number of coloured regions within the circle.
This then shows the red area in any circle, with any number of regions.