Answer:
[tex]105.84\ cm^2[/tex]
Step-by-step explanation:
step 1
Find the area of the circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=21.2/2=10.6\ cm[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (10.6)^{2}[/tex]
[tex]A=112.36\pi\ cm^2[/tex]
step 2
Find the area of a sector
Remember that
The area of the circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of a sector with a central angle of 108 degrees
[tex]\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]33.708(3.14)=105.84\ cm^2[/tex]
