Q. 203.7( 15 Votes )
Rabeya drew an equilateral triangle with sides 21 cm. on a big paper. Drawing a circle inscribing that triangle coloured the circular region. I write by calculating the area of coloured region.
Answer :
Given: Length of side of equilateral triangle = 21 cm
Area of the colored portion = Area of the circum circle - Area of ∆BCD
Height of equilateral triangle 
The centroid of equilateral triangle is at A and lies on height BE.
⇒ BA = 7√3 cm
So, the radius of the circum circle of this triangle = 7√3 cm.
∵ Area of a circle = πr2
Area of the circum circle
⇒ Area of the circum circle = 462 cm2
We know that
Area of a equilateral triangle 
where a is the side of it.
⇒ Area of ∆BCD = 190.96cm2
Now, Area of the colored portion = 462 – 190.96
⇒ Area of the colored portion = 271.04 cm2
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