Generalisating
Pretend the number of parts is 'n' and the radius of the smallest semi-circle is 'a'. To find the radius of the whole circle you would use the formula: n x a. So to find the diameter, excluding the red part,(F) the formula would be 2 x n x a - 2 x a.
Therefore F would be n x a - a x 1 = a x (n - 1). Lets call a x (n - 1), 'b'.
b x pi x 1/2 = the area of the bottom semi-circle excluding the red part.
n x a x a x a x pi x 1/2 = the bottom semi-circle.
b x pi x 1/2 - n x a x a x a x pi x 1/2 = the bottom part of red.
a x a x 1/2 x pi = the top part of red.
The sum of the above 2 lines equals the area of the red part.
Proportion
The proportion of red to the circle, which is made up of three parts, is 1/3. To prove this theory: After you have found the area of red (using the method above) you would see that the area of red is 1/3 of the area of the whole circle. Since the red part equals the yellow part; therefore, the orange part would equal the other two. Meaning the red part is 1/3.