Three equal circles, each of radius 6 cm, touch one another.find the area enclosed between them.

Three equal circles, each of radius 6 cm, touch one another.find the a

1.	Three equal circles, each of radius 6 cm, touch one another.find the area enclosed between them.
Answer» Let A, B, C, be the centres of these circles. Joint AB, BC, CA. Radius of each circle = 6cm . AB = BC = CA = 12 cm .Then,ABC is an equilateral triangle.Then, Area of ∆ABC,{tex}=\\frac{\\sqrt3}{4}×(side)^2\\\\ =\\frac{\\sqrt 3}{4}×(12)^2\\\\ =\\frac{\\sqrt 3}{4}×(12)×(12)\\\\ =36×1.73=62.28{/tex}Area of sector of angle 60° and radius 6 cm{tex}=\\frac{\\theta}{360}×πr^2\\\\{/tex}{tex} =\\frac{60}{360}×3.14×6×6\\ cm^2=18.84\\ cm^2{/tex}Required area = Area of ∆ABC- 3 ×area of one sector {tex}{/tex}\xa0{tex}{/tex}{tex}{/tex}=62.28-3× 18.84{tex}{/tex} =(62.28- 56.52) cm{tex}^2{/tex}{tex}{/tex}=5.76 cm{tex}^2{/tex}{tex}{/tex}Area of shaded region = 5.76 cm2