Find area of green sections- please help!!

[bczerwonka]

 

[Deleted member 4993]

View attachment 17642

Name vertices of the equilateral triangle (A, B & C) and center of circles (concentric) O.

let the diameter of the little circle be 'd'.

Then drop a perpendicular to one side of the triangle (AB) from the center.

Let the perpendicular intersect AB at D

The contained angle of sector AOB = 2/3 * \(\displaystyle \pi \) ...... continue


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[Dr.Peterson]

You can also observe that the green, blue, and magenta regions all have the same area; so there's not much work left after you find the radius of the inner circle ...