Answer:
[tex]37.01\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=20.6/2=10.3\ mm[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(10.3^{2})=333.1226\ mm^{2}[/tex]
[tex]2\pi[/tex] radians subtends the complete circle of area [tex]333.1226\ mm^{2}[/tex]
so
by proportion
Find the area of a sector with a central angle of [tex]2\pi/9[/tex] radians
[tex]\frac{333.1226}{2\pi}=\frac{x}{2\pi/9}\\ \\x=336.1226*( 2\pi/9)/(2\pi)\\ \\x=37.01\ mm^{2}[/tex]
