Given,
Radius of circle 1 = r1 = 19 cm
Radius of circle 2 = r2 = 9 cm
We know that, the circumference of a circle (C) = 2πr
So, C1 = 2πr1 and C2 = 2πr2
Let the radius be r of the circle which is to be found and its circumference (C)
Now, from the question
C = C1 + C2
2πr = 2πr1 + 2πr2
r = r1 + r2 [After dividing by 2π both sides]
r = 19 + 9
r = 28 cm
Thus, the radius of the circle = 28 cm
So, the area of required circle = πr2 = (22/7) × 28 × 28 = 2464 cm2