Question

In following figure, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region). `["Use" pi=22/7]`

Answer 1

The given information can be diagrammatically represented as follows: 

Here, A, B and C are the centres of the circles. 

Radius of each circle, r = 3.5 cm 

Thus, the measure of each of the sides of ΔABC is 3.5 cm + 3.5 cm = 7 cm. 

Since the sides of triangle ABC are of equal lengths, it is an equilateral triangle. 

∴ ∠A = ∠B = ∠C = 60° 

Area of the shaded region = Area of ΔABC − (sum of areas of sectors APR, BPQ and CQR) 

`=sqrt3/4a^2-3xxO//360^@xxpir`

`=1.732/4xx(7"cm")^2-3xx60^@/360^@xx22/7xx3.5"cm"xx3.5"cm"`

`=21.217 "cm"^2-19.25cm^2`

`=1.97"cm"^2`