Answer
The capacitance is $~~8.41\times 10^{-12}~F$
Work Step by Step
We can find the capacitance of the left half of the capacitor:
$C = \frac{\kappa_1~\epsilon_0~A/2}{d}$
$C = \frac{(7.00)(8.854\times 10^{-12}~F/m)(2.78\times 10^{-4}~m^2)}{5.56\times 10^{-3}~m}$
$C = 3.0989\times 10^{-12}~F$
We can find the capacitance of the right half of the capacitor:
$C = \frac{\kappa_1~\epsilon_0~A/2}{d}$
$C = \frac{(12.0)(8.854\times 10^{-12}~F/m)(2.78\times 10^{-4}~m^2)}{5.56\times 10^{-3}~m}$
$C = 5.3124\times 10^{-12}~F$
Note that the two parts are in parallel.
We can find the equivalent capacitance:
$C_{eq} = 3.0989\times 10^{-12}~F+5.3124\times 10^{-12}~F$
$C_{eq} = 8.41\times 10^{-12}~F$
The capacitance is $~~8.41\times 10^{-12}~F$
