An amplitude modulated (AM) radio wave bends noticeably around the...

For diffraction (bending of waves around corners) to be noticeable, the wavelength of the wave must be comparable to or greater than the size of the obstacle.

Since the AM wave bends noticeably around the $1 \text{ m} \times 1 \text{ m}$ board, its wavelength $\lambda_a$ must be comparable to or greater than $1 \text{ m}$.

Since the FM wave bends negligibly, its wavelength $\lambda_f$ must be smaller than the dimensions of the board.

Therefore, $\lambda_a > \lambda_f$.

This is also consistent with typical radio frequencies, where AM operates around $1 \text{ MHz}$ ($\lambda_a \approx 300 \text{ m}$) and FM operates around $100 \text{ MHz}$ ($\lambda_f \approx 3 \text{ m}$).