We should take the length and the expansiveness of the square shape be x m and y m.

Thus, the edge \[=\text{ }2\left( x\text{ }+\text{ }y \right)\text{ }m\]

\[104\text{ }=\text{ }2\left( x\text{ }+\text{ }y \right)\]

\[x\text{ }+\text{ }y\text{ }=\text{ }52\]

\[y\text{ }=\text{ }52\text{ }\text{ }x\]

Also, given region \[=\text{ }640\text{ }m2\]

Thus, \[xy\text{ }=\text{ }640\]

\[x\left( 52\text{ }\text{ }x \right)\text{ }=\text{ }640\]

\[x2\text{ }\text{ }52x\text{ }+\text{ }640\text{ }=\text{ }0\]

\[x2\text{ }\text{ }32x\text{ }\text{ }20x\text{ }+\text{ }640\text{ }=\text{ }0\]

\[x\left( x\text{ }\text{ }32 \right)\text{ }\text{ }20\text{ }\left( x\text{ }\text{ }32 \right)\text{ }=\text{ }0\]

\[\left( x\text{ }\text{ }32 \right)\text{ }\left( x\text{ }\text{ }20 \right)\text{ }=\text{ }0\]

\[x\text{ }=\text{ }32,\text{ }20\]

In the event that \[x\text{ }=\text{ }32,\text{ }y\text{ }=\text{ }52\text{ }\text{ }32\text{ }=\text{ }20\]

Or on the other hand if \[x\text{ }=\text{ }20,\text{ }y\text{ }=\text{ }52\text{ }\text{ }20\text{ }=\text{ }32\]

Accordingly, the length and expansiveness of the square shape are \[32\text{ }m\text{ }and\text{ }20\text{ }m.\]