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Alenkinab [10]
2 years ago
10

Please help. You get imaginary money if you help

Mathematics
1 answer:
Lorico [155]2 years ago
8 0

Answer:

  • perimeter: 73.81 in
  • area: 284.955 in²

Step-by-step explanation:

You want to find the perimeter and area of a sector that is 3/4 of the circle. The perimeter will be the sum of twice the radius and the length of the arc. The area will be 3/4 of the area of the full circle.

__

<h3>Perimeter</h3>

The length of a circular arc is ...

  s = rθ . . . . . where θ is the central angle in radians

  s = (11 in)(3/2π) . . . . . . . a 3/4 circle has a central angle of 3/2 radians

  s = (11 in)(3/2)(3.14) = 51.81 in

When we add the two radii to this, we get a total perimeter of ...

  P = 2r +s = 2(11 in) +51.81 in = 73.81 in . . . . perimeter of the figure

__

<h3>Area</h3>

The area of a sector is given by the formula ...

  A = 1/2r²θ . . . . . where r and θ are the radius and central angle (in radians)

  A = 1/2(11 in)²(3/2π) = (1/2)(121 in²)(3/2)(3.14)

  A = 284.955 in² . . . . area of the figure

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