I entered the area of the field into a Pythagorean Theorem Calculator and it concluded that the diagonal length of the field would be approximately 750 yard.
The length of the diagonal of the field is found using the Pythagorean Theorem and is
d = √( 450 yd)² + ( 600 yd)² ) = √562500 yd² = 750 yd is the diagonal distance. If, on the other hand, the farmer walks the length and width of the perimeter of the field, that would be 450 yd + 600 yd, or 1050 yd.
The farmer could spare himself 1050 - 750, or 300 yd, of walking if he crosses the field along a diagonal.
