Point \(Y\) lies on line segment \(\overline{XZ} \) such that \(XY = 2\) and \(YZ = 4.\) Semicircles are constructed with diameters \(\overline{XY}\), \(\overline{XZ}\), and \(\overline{YZ}\). Find the area of the blue region.
Semi circle areas are 1/ 2 pi r^2
calculate the largest one (r = 6) ....and subtract the two smaller ones ( r= 2 and 4)
1/2 pi ( 6^2 - 2^2 - 4^2)
1/2 pi ( 16) = 8 π units2