O1O2O3 is equilateral triangle of side length 12 cm.
\(\therefore\) Area of \(\triangle O_1O_2O_3 = \frac{\sqrt3}4 a^2\)
\(= \frac{\sqrt 3}4 \times {12}^2 = \frac{\sqrt 3}4 \times 144 = 36\sqrt3 \,cm^2\)
\(\approx 62.35 \,cm^2\)
Area of sector O1AC = Area of sector O2AB = Area of sector O3BC
\(= \frac{60°}{360°}\times \pi r^2 \)
\(= \frac 16 \times 3.14 \times 6^2\)
\(= 18.84 cm^2\)
\(\therefore\) Area enclosed between three circles = Area of \(\triangle\)O1O2O3 - 3 x Area of sector O1AC
\(= 62.35 - 3 \times 18.84\)
\(= 62.35 - 56.52\)
\(= 5.83 \, cm^2\)
