To answer this question, you need to find the area of the divided land that the farmer want. Since it was a square with 1/4 mile length then the area would be:
1/4 mile * 1/4 mile= 1/16 miles square.
Then you can divide the total area of land the farmer buys, with the area of divided land. The calculation would be: (1/2 square miles) / (1/16 square miles)= 16/2=8 pieces of field