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Minor arc AB in the diagram is 30 and the radius of the circle is 6. Find the area of circular segment AB.

 Feb 22, 2022
 #1
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What diagram?

 Feb 23, 2022
 #2
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I couldn't attach it, but I think it's still possible to solve without it.

 

If you need the description, here it is:

 

It's a circle with center O and B and A are two points on the edge of the circle (B comes before A when clockwise).

Guest Feb 23, 2022
 #3
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The area of the segment is 6*pi - 12.

 Feb 23, 2022
 #4
avatar+2444 
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Oh wait, never mind, I think I know how to solve it. 

 

The circular segment is equal to the area of the region \(ABO-\triangle{ABO}\)

 

We know the circular region's area is \({30 \over360} \times 36\pi =3\pi\)

 

\(\triangle{ABO}\) is isosceles, with degrees of 30, 70, 70, and 2 sides with 6. Using trig, we find that the area of the triangle is 9. 

 

Thus, the area of the circular region is: \(\color{brown}\boxed{3\pi - 9}\)

 Feb 24, 2022

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