The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]
We want to find the area of the blue sector.
First, let's find the angle of the sector. This angle and angle 84 are in a straight line. Thus, we can say:
[tex]\theta+84=180[/tex]
Where θ is the angle of the sector.
Let's solve for θ:
[tex]\begin{gathered} \theta+84=180 \\ \theta=180-84 \\ \theta=96 \end{gathered}[/tex]
We also recognize that BD is the diameter and BA is the radius.
We know
Radius is HALF of Diameter.
Given,
Diameter = 6
Radius = 6/2 = 3
Now, let's calculate the area of the sector:
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ A=\frac{96}{360}\times\pi(3)^2 \\ A=\frac{4}{15}\times9\pi \\ A=\frac{36\pi}{15} \end{gathered}[/tex]
Rounded to 2 decimal places,
Answer
Area = 7.54 sq. cm.
