In the diagram, K, O and M are the centers of the three semi-circles. OC = 32 and CB = 38,
What is the area of the semi-circle with center k?
+526 Consider this labelled diagram
It's given that \(OC=32 \) and \(CB=38\)
⇒\(OB = OC+CB\)
\(=32+38\)
\(=70 \)
Radius of semi-circle (3) is \(70\).
And, CB is diameter of semi-circle (2).
So, radius of semi-circle is \(38/2=19\).
From figure, we can infer that
Ar. (semi-circle 1) = Ar. (semi-circle 3) - Ar. (semi-circle 2)
\(= {4900\pi \over 2} - {361\pi \over 2}\)
\(={4539\pi \over 2}\)
\(=7126.23\) sq. units
Thus, the area of circle with centre K is \(7126.23\) sq. units.
~Amy 
