The area of the unshaded region of the circle will be 120π units squared.
The area of a sector of a circle of radius r having an angle a° is given by:
Area of sector = (π*[tex]r^{2}[/tex])*(a°/360°) units squared.
Given ∡KLM = 60°. The radius of the circle is 12 units.
⇒The area of shaded sector KLM = (π*[tex]12^{2}[/tex])*(60°/360°) = π·144/6 = 24π sq. units.
The area of the unshaded region of the circle = (total area of the circle) - (the area of sector KLM) = (π*[tex]12^{2}[/tex]) - 24π = 120π sq units.
∴ The area of the unshaded region of the circle is 120π units squared.
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