What is the area of the Shaded Region?

Question

I need help figuring out what the area of the shaded part is.
Answer needs to be in at least 2 decimal places.

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Answer 1 · 2018-05-07T00:05:32

#A_("Shaded Region")i=603.19# square feet

.

The three central angles are shown to be equal. Therefore, each is #360/3=120^@#.

The area of the shaded region is #1/3# of the area of the circle.

#A_("Circle")=pir^2=pi(24)^2=576pi# square feet

#A_("Shaded Region")=(576pi)/3=192pi=603.19# square feet

Answer 2 · 2018-05-07T00:19:01

#A = 603.19 ft^2#

The angle of a circle is #360# degrees. Since the sectors are equally split in three, then the angle is #360/3 = 120#.

To calculate the area of a sector, you apply this formula:

#A = (theta)/360 pir^2#

The angle #theta# is 120 and the radius #r# is 24ft.

#A = 120/360 *24^2 pi#

#A = 603.19#