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

Find the areas of the sectors formed by < DFE. Round to the nearest hundredth-example-1

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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.

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.

User Cpalmer
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