A point charge q is placed at a distance a/2 directly above the center of a square of side a. The total electric flux through the square is:

Imagine the square as one of the six faces of a cube of side $a$ with the charge $q$ placed at its exact center. By Gauss's law, total flux through all six faces of the cube is $\Phi_{\text{total}} = \frac{q}{\varepsilon_0}$. By symmetry, the flux through each face (including the given square) is $\frac{1}{6}$th of the total flux, i.e., $\frac{q}{6\varepsilon_0}$.