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How do you solve for the segment area in a circle?

How do you solve for the segment area in a circle?-example-1

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9514 1404 393

Answer:

36.23 square meters

Explanation:

The area of a segment that subtends central angle α (in radians) is given by the formula ...

A = (1/2)r²(α -sin(α))

Your sector has α = π/3, so the area is ...

A = (1/2)(20 m)²(π/3 -sin(π/3)) ≈ (200 m²)(1.04720 -0.86603)

A ≈ 36.23 m²

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Additional comment

The segment area formula represents the difference between the sector area and the triangle area.

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