Answer:
3 m^2
Step-by-step explanation:
The shaded area = Area of Sector - Area of Triangle
First we find area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]
We know the angle is 60° (vertical angles are equal) and the radius is 6, so we find the area of sector to be:
[tex]\frac{\theta}{360}*\pi r^2\\\frac{60}{360}*\pi (6)^2\\=18.85[/tex]
Secondly, we find area of triangle (isosceles) = [tex]\frac{1}{2}abSinC[/tex]
where
a and b are the two sides bordering the known angle, so a=b=6, and
C is the angle which is 60°
Now we find the area to be:
[tex]\frac{1}{2}(6)(6)Sin(60)\\=15.59[/tex]
Hence, area of shaded = [tex]18.85 - 15.59=3.26[/tex]
Rounding to nearest whole number, area of shaded region = 3m^2
