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Let each side of the triangle be a cm . Then,
Area of the triangle = ( √3/4 × a² ) cm².
Therefore,
√3/4 × a² = 100√3
a² = 400
a = √400
a = 20 cm.
Thus , the length of each side of a ∆ ABC is 20 cm.
Therefore,
Radius of each circle = 10 cm.
Required area = ( Area of ∆ ABC ) - 3 ( Area of a sector with r = 10 cm , ¢ = 60° )
=> ( 100√3 - 3 × 3.14 × 10 × 10 × 60/360 ) cm².
=> { ( 100 × 1.732 ) - 157 } cm².
=> ( 173.2 - 157 ) cm².
=> 16.2 cm².
Hence,
The area of the required part is 16.2 cm².
Area of the triangle = ( √3/4 × a² ) cm².
Therefore,
√3/4 × a² = 100√3
a² = 400
a = √400
a = 20 cm.
Thus , the length of each side of a ∆ ABC is 20 cm.
Therefore,
Radius of each circle = 10 cm.
Required area = ( Area of ∆ ABC ) - 3 ( Area of a sector with r = 10 cm , ¢ = 60° )
=> ( 100√3 - 3 × 3.14 × 10 × 10 × 60/360 ) cm².
=> { ( 100 × 1.732 ) - 157 } cm².
=> ( 173.2 - 157 ) cm².
=> 16.2 cm².
Hence,
The area of the required part is 16.2 cm².
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