Question

Three equal circle of radius 3 cm touch one another. Find the area enclosed by them.

Answer 1

Since the radius of the circles are equal and the circles touch one another, in the figure, ABC is an equilateral triangle and the area of the sectors DAF, DBE and ECF are equal. Hence,

Area enclosed = area of the equilateral triangle ABC - 3 times area of the sector

$=\frac{\sqrt{3}}{4}{a}^2-3\times \frac{\theta }{{360}^{\circ }}\times \pi r^2$

$=\frac{\sqrt{3}}{4}\times 6\times 6-3\times \frac{{60}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 3\times 3$

$=9\sqrt{3}-\frac{99}{7}=15.59–14.14=1.45c{m}^2$

$Area=1.45c{m}^2$