Q19 of 35 Page 311

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.

Given: ∆ABC is an equilateral triangle with side 10 cm, Arcs centered at B and C have radius 5 cm.


We need to find the area of the colored portion.


Area of colored portion = Area of ∆ABC – Area of sectors centered at B and C.


∵ ∆ABC is an equilateral triangle


We know that


Area of a equilateral trianglewhere a is the side of it.



⇒ Area of ∆ABC = 43.3cm2


For the sectors,


Radius = 5 cm and angle subtended = 60°


{∵∆ABC is an equilateral triangle and each angle of it is 60°}


We know that the area of the minor sector


⇒ Area of sector centered at


⇒ Area of sector centered at B =13.095 cm2


Total area of both the sectors centered at B and C = 13.095 + 13.095 = 26.19 cm2


⇒ Area of colored portion = 43.3 – 26.19 = 17.11 cm2


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