Q. 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.


Answer :

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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