anonymous
  • anonymous
Find the area of the shaded portion in the equilateral triangle with sides 6. (assuming the central point of each arc is its corresponding vertex)
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1 Attachment
UnkleRhaukus
  • UnkleRhaukus
The shaded region is the area of a triangle minus three circular sectors
UnkleRhaukus
  • UnkleRhaukus
We know the triangle is equilateral - so all the angles are 60°

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UnkleRhaukus
  • UnkleRhaukus
|dw:1370407194893:dw|
UnkleRhaukus
  • UnkleRhaukus
|dw:1370407262610:dw| \[3^2+h^2=6^2\\h=\sqrt{6^2-3^2}\]
UnkleRhaukus
  • UnkleRhaukus
The total area of the equilateral triangle is \[A_\text{triangle}=\frac12bh=\frac12\times6\times h\]
UnkleRhaukus
  • UnkleRhaukus
The area of a circle \[A_\text{circle}=πr^2\] The area of a sector is \[A_\text{sector}=\frac{θ°}{360°}×πr^2\] The angle in your three sectors is 60°, and the radius is 3

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