In the diagram, \(K\), \(O\) and \(M\) are the centers of the three semi-circles. Also, \(OC = 32\) and \(CB = 36\) .What is the area of the semi-circle with center \(K\)?
OB = OC + CB = 32 + 36 = 68
AB = 2 * OB = 2 * 68 = 136
AC = AB - CB = 136 - 36 = 100
diameter of circle K = AC = 100
radius of circle K = 100/2 = 50
area of semicircle K = (1/2)(pi)(502) = 1250pi sq units
Thank you so much, hectictar!
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