In the Public Land Survey System, the dimensions and area of a ¼ - section?

In the Public Land Survey System, the dimensions and area of a ¼ - section?

• A. ½ mile x ½ mile; ¼ square mile or 160 acres
• B. ¼ mile x ¼ mile; 1/16 square mile
• C. 1 mile x 1 mile; 1 square mile
• D. 3/4 mile x 3/4 mile; 9/16 square mile

Answer: (A)

In the Public Land Survey System, a section is a square mile, which is 640 acres. A quarter-section is one-fourth of that area, so its acreage is 640 ÷ 4 = 160 acres. To keep a square shape, the side length must be half a mile, giving dimensions of 1/2 mile by 1/2 mile. A square with those side lengths has area (1/2) × (1/2) = 1/4 square mile, which is 160 acres. That matches the description of half a mile on each side and an area of one-quarter of a square mile (160 acres). The other options describe incorrect dimensions or areas for a quarter-section: for example, 1/4 mile by 1/4 mile would be 1/16 square mile (40 acres); 1 mile by 1 mile is a full section (1 square mile); and 3/4 mile by 3/4 mile is 9/16 square mile.

In the Public Land Survey System, a section is a square mile, which is 640 acres. A quarter-section is one-fourth of that area, so its acreage is 640 ÷ 4 = 160 acres. To keep a square shape, the side length must be half a mile, giving dimensions of 1/2 mile by 1/2 mile. A square with those side lengths has area (1/2) × (1/2) = 1/4 square mile, which is 160 acres.

That matches the description of half a mile on each side and an area of one-quarter of a square mile (160 acres). The other options describe incorrect dimensions or areas for a quarter-section: for example, 1/4 mile by 1/4 mile would be 1/16 square mile (40 acres); 1 mile by 1 mile is a full section (1 square mile); and 3/4 mile by 3/4 mile is 9/16 square mile.