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Alexus [3.1K]
2 years ago
12

Find the area of the shaded segment of the circle. Please help

Mathematics
1 answer:
natka813 [3]2 years ago
5 0

Answer:

  1.4 m²

Step-by-step explanation:

The area of a sector with central angle θ (in radians) is given by the formula

  A = (1/2)r²θ

The area of the triangle with central angle θ is given by the formula

  A = (1/2)r²sin(θ)

The area of the shaded segment is the difference of these:

  A = (1/2)r²(θ -sin(θ))

Your segment has a central angle of 60° = π/3 radians, so its area is ...

  A = (1/2)(4 m)²(π/3 -sin(π/3)) = (8 m²)(π/3 -(√3)/2)

  A ≈ 1.4 m²

The area of the shaded segment is about 1.4 m².

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