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. 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 triangle where 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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