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Since both the circles are symmetric, we use the formula .
Here, is the angle subtended by the common chord at any one of the centres.
We have, . Then the common area, .

Let the circumference intersect at point A and B. Radius=r=1cm The common cord will make a center angle Ф=120 degree The common area is sum of the two segments with common cord AB. Due to symmetry of circle both the segments are equal. We have the area of segment= r²(π*Ф/180 - sinФ)/2 The common area=2*r²(π*Ф/180-sinФ)/2 ⇒1²(π*120/180 - sin120) ⇒ 2π/3 - 0.5806 ⇒2.0943- 0.5806 ⇒ 1.513 cm²