Three equal circles, each of radius 6 cm, touch one another as shown in the figure. Find the area of enclosed between them.
Join ABC. All sides are equal, so it is an equilateral triangle.
Now,
Area of the equilateral triangle $=\frac{\sqrt{3}}{4} \times \operatorname{Side}^{2}$
$=\frac{1.73}{4} \times 12 \times 12$
$=62.28 \mathrm{~cm}^{2}$
Area of the arc of the circle $=\frac{60}{360} \pi \mathrm{r}^{2}$
$=\frac{1}{6} \pi r^{2}$
$=\frac{1}{6} \times \frac{22}{7} \times 6 \times 6$
$=18.86 \mathrm{~cm}^{2}$
Area of the three sectors $=3 \times 18.86=56.57 \mathrm{~cm}^{2}$
Area of the shaded portion = Area of the triangle
$=62.28-56.57$
$=5.71 \mathrm{~cm}^{2}$
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