1. **Problem statement:** A block of density $\rho_B$ with horizontal cross-sectional area $A$ and height $h$ floats in a fluid of density $\rho_f$. It is pushed down and released. We want to find which quantity does *not* affect the frequency of the simple harmonic motion (SHM) it executes. 2. **Relevant formula:** The frequency $f$ of SHM for a floating block is given by $$f = \frac{1}{2\pi} \sqrt{\frac{\rho_f g A}{\rho_B h A}} = \frac{1}{2\pi} \sqrt{\frac{\rho_f g}{\rho_B h}}$$ where $g$ is acceleration due to gravity. 3. **Explanation:** The frequency depends on the fluid density $\rho_f$, block density $\rho_B$, gravitational acceleration $g$, and height $h$. The cross-sectional area $A$ cancels out in the formula. 4. **Intermediate step showing cancellation of $A$:** $$f = \frac{1}{2\pi} \sqrt{\frac{\rho_f g \cancel{A}}{\rho_B h \cancel{A}}}$$ 5. **Conclusion:** The quantity that has nothing to do with the frequency is the cross-sectional area $A$. **Final answer:** (C) $A$