Question

Find the areas of the sectors formed by < DFE. Round to the nearest hundredth

Answer 1

The area of the orange sector is 10.47 square feet, approximately.

The area of the blue sector is 39.77 square feet, approximately.

Explanation:

We know that
`\angle DFE = 75\°`.

Now, the area of a circular sector can be found with the formula

`Sector =\pi r^(2) * (\theta)/(360\°)`

In this case,
`\theta = 75\°` and
`r=4 ft`.

Replacing the angle and the radius, we have

`S_(orange)=3.14(4)^(2) * (75)/(360)= 10.47 ft^(2)`

Therefore, the area of the orange sector is 10.47 square feet, approximately.

Now, the blue sector has a central angle of
`360-75 = 285\°`. So, its area is

`S_(blue)=3.14(4)^(2) * (285)/(360) \approx 39.77ft^(2)`

Therefore, the area of the blue sector is 39.77 square feet, approximately.