The capacitance of a parallel plate capacitor which has plates of area A, a distance of separation of the plates equal to d and the permittivity epsilon is equal to e, is given by the formula

C = e*A / d

Here we are given that the capacitance of the capacitor is 1 F. The plates are separated by a distance equal to 1.7 mm and e = 8.85*10^-12. Substituting the given values in the formula we get

1 = 8.85*10^-12 * A / 1.7*10 ^-3

=> A = 1.7* 10^-3 / 8.85* 10^-12

=> A = 192.09 * 10^6 m^2

=> 192.09 km^2

The area of the plates in square kilometers is 192.09.