We need to find the area of a sector of circle, bounded by a 114° arc. That sector is a fraction of the circumference, let's calculate it:
We have an arc of 114°, while the complete circumference has 360°.
The fraction of circle from we are going to calculate the area is:
[tex]\frac{114}{360}[/tex]
Now, we can estimate the total area of the circle of radius 6, and then multiply it by the fraction of circumference that concerns us: 114/360.
The area of the cicle is:
[tex]\pi\cdot r^2=\pi\cdot(6m)^2=36\pi m^2[/tex]
Now, the area of the sector is:
[tex]A=\frac{114}{360}\cdot36\pi m^2[/tex]
360 is ten times 36, so:
[tex]A=\frac{114}{10}\pi m^2[/tex]
Now simplifying, the half of 114 is 57, while the half of 10 is 5, then:
[tex]A=\frac{57}{5}\pi m^2[/tex]
