A field in the form of a rhombus has each side of length 64 m and altitude 16 m.

Given:

Each side of a rhombus shaped field $=64 \mathrm{~m}$

Altitude $=16 \mathrm{~m}$

We know: Area of rhombus $=$ Side $\times$ Altitude

$\therefore$ Area of the field $=64 \times 16=1024 \mathrm{~m}^{2}$

Given: Area of the square field $=$ Area of the rhombus

We know: Area of a square $=(\text { Side })^{2}$

$\therefore 1024=(\text { Side })^{2}$ $\Rightarrow$ Side $=\sqrt{1024}=32 \mathrm{~m}$

Thus, the side of the square field is $32 \mathrm{~m}$.