Radius of 1^{st} circle = 19 cm

Radius of 2^{nd} circle = 9 cm

Circumference of 1^{st }circle = 2π(19) = 38π cm

Circumference of 2^{nd} circle = 2π (9) = 18π cm

Let radius of required circle = R cm

Circumference of required circle = 2πR = c_{1}+c_{2}

2πR = 38π + 18π

2πR = 56π

R = 28 cms

Area of required circle = πr^{2}

=22/7 x 28 x 28

=2464 cm^{2}