Q20 of 35 Page 311

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


More from this chapter

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18

Buying a bangle from fair Nila wears in her hand. The Bangle contains 269.5 sq. cm. metal. If the length of outer diameter of bangle is 28 cm, let us write by calculating the length of inner diameter.

 19

Protul has drawn an equilateral triangle ABC picture beside of which length of each side is 10 cm. Sumita has drawn three circular arcs centering A, B, C with the length of radius 5 cm. and has coloured some portion at the middle. Let us write by calculating the area of coloured portion.

 21

The area of circumscribing circular region of an equilateral triangle is 462 sq. cm. Let us write by calculating length of each side of this triangle.

 22

Perimeter of a triangle is 32 cm. and area of inscribing circle is 38.5 sq. cm. Let us write by calculating the area of this triangle.