What is the area of the Shaded Region?

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

2 Answers
May 7, 2018

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

Explanation:

.

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

May 7, 2018

A = 603.19 ft^2

Explanation:

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