Find Area of Circle Segments: Chord Length 4cm, Radius 3.3cm

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SUMMARY

The discussion centers on calculating the area of circle segments created by a chord of length 4cm in a circle with a radius of 3.3cm. The initial calculation of one segment's area was approximately 1.84 cm², but the user incorrectly applied the formula for the area of a circle to find the second segment's area, resulting in a discrepancy with the answer booklet. The correct approach involves using the area of the isosceles triangle formed by the radius lines to the chord's endpoints and the angle between them to accurately determine the segment area.

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  • Knowledge of the area formula for triangles
  • Familiarity with the concept of circle segments
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  • Learn how to calculate the area of circle segments using the formula: Area = (r²/2) * (θ - sin(θ))
  • Study the properties of isosceles triangles and their area calculations
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A chord of length 4cm divides a circle of radius 3.3cm into two segments. Find the area of each segment.

I've managed to workout the area of one of the segments (approx 1.84 cm^2). This is the correct solution given in my answer booklet.

The second segment area would therefore be 2*pi*(3.3)^2 - 1.84 = 66.58 cm^2.

But my answer booklet says its: 32.38 cm^2.

Can someone point me in the right direction on this one because I'm completely lost.

Thanks.

Oops, I've just realized.. wrong equation for the area of a circle. Don't bother with this question.
 
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Why did you do 2*pi*r^2 for the area of the second segment?
 
Draw the radius lines to each end of the chord. This creates an isosceles triangle.
You should be able to determine both the area of the triangle and the angle between the radius lines.

Use that information to determine the area of the segment bounded by the chord.
 

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