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### Best Answer dezalyx says

Because the triangle is equilateral, the angle for the pink area is 60 degrees, which is 1/6 of the 360 degree circle. So the area of the pink shaded region is pi * r^2 / 6.

The height of the triangle is sqrt (4 - 1) = sqrt (3). Which makes the area of the whole triangle= sqrt (3) * 2 / 2 = sqrt (3). So the area of the green shaded region = area of the whole triangle - area of the pink shaded region = sqrt (3) - pi * r^2 / 6.

Given that the area of the pink shaded region = area of the green region, we get the following equation:

pi * r^2 / 6 = sqrt (3) - pi * r^2 / 6

Solving for r:

pi * r^2 / 3 = sqrt (3)

r^2 = 3 * sqrt (3) / pi

r = sqrt [3 * sqrt (3) / pi]

### GreenMathDr says

Since the area of the triangle is sq rt 3, then pi r^2/6 must equal (rad 3)/2. cross multiplying and dividing by 3 and simplifying gives approximately 1.654 = r^2 taking the sq rt of each side gives approximately 1.286.