In the given figure three circles, each of radius 3.5 cm are placed in such a way that each circle touches the other two.

The area of the portion enclosed by the circles is: (Up to two decimal places) (Use π = )

Given Data:

Radius of each circle = 3.5 cm

Concept Used:

The area of the circle = πr²

The area of an equilateral triangle = √3/4 × side²

Calculation:

The side of the equilateral triangle formed by the centers of the circles,

⇒ 2 × radius = 2 × 3.5 cm = 7 cm

The area of this equilateral triangle,

⇒ √3/4 × (7 cm)2 = 49√3/4 = 1.73(49/4) cm2 

The area of each sector with an angle of 60 degrees in the three circles,

⇒ (60/360) × π × (3.5 cm)2

The area of all the three sectors combined = 3 × (60/360)×π×(3.5 cm)2

⇒ π × (35/10) × (35/10) × 180/360

⇒ 3.14 × 1/2 × 7/2 × 7/2

⇒ 1.57 × 49/4 cm2

The area of the portion enclosed by the circles = Area of the equilateral triangle - Area of the three sectors

⇒ 1.73(49/4) -   1.57 × 49/4 

⇒ (1.73 - 1.57) 49/4

⇒ 0.16 × 12.25

⇒ 1.97 cm2

Therefore, the area of the portion enclosed by the circles is approximately 1.97cm2.