Answer:
The area of the orange sector is 10.47 square feet, approximately.
The area of the blue sector is 39.77 square feet, approximately.
Step-by-step explanation:
We know that [tex]\angle DFE = 75\°[/tex].
Now, the area of a circular sector can be found with the formula
[tex]Sector =\pi r^{2} \times \frac{\theta}{360\°}[/tex]
In this case, [tex]\theta = 75\°[/tex] and [tex]r=4 ft[/tex].
Replacing the angle and the radius, we have
[tex]S_{orange}=3.14(4)^{2} \times \frac{75}{360}= 10.47 ft^{2}[/tex]
Therefore, the area of the orange sector is 10.47 square feet, approximately.
Now, the blue sector has a central angle of [tex]360-75 = 285\°[/tex]. So, its area is
[tex]S_{blue}=3.14(4)^{2} \times \frac{285}{360} \approx 39.77ft^{2}[/tex]
Therefore, the area of the blue sector is 39.77 square feet, approximately.
