Answer:
37.03 sq. mm.
Step-by-step explanation:
A sector is "part" of a circle. The formula for area of a sector (in radians) is:
Area of sector = [tex]\frac{1}{2}r^2 \theta[/tex]
Where
r is the radius (half of diameter)
[tex]\theta[/tex] is the central angle of the sector
In this problem, the diameter is given as 20.6, so radius would be:
Radius (r) = 20.6/2 = 10.3
The central angle is given as [tex]\frac{2\pi}{9}[/tex] radians
Now, we substitute and find the value for the area:
[tex]A=\frac{1}{2}r^2 \theta\\A=\frac{1}{2}(10.3)^2 (\frac{2\pi}{9})\\A=\frac{1}{2}(106.09)(\frac{2(3.14)}{9})\\A=53.045*0.698\\A=37.03[/tex]
Thus,
Area of sector = 37.03 sq. mm.
