# 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.

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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