A square mile consists of 640 acres. Therefore, a square 1/2 mile is how many acres?

A square mile consists of 640 acres. Therefore, a square 1/2 mile is how many acres?

• A. 80 acres
• B. 320 acres
• C. 160 acres
• D. 640 acres

Answer: (C)

When you change a length and want to know the area in different units, remember that area scales with the square of the linear dimension. A square mile equals 640 acres, so convert the smaller square’s area to square miles first, then to acres. A square half a mile on each side has area (1/2) × (1/2) = 1/4 of a square mile. Convert to acres: 1/4 × 640 = 160 acres. That’s why the amount is 160 acres. The other numbers correspond to different sized areas (for example, 320 acres is half a square mile, and 640 acres is a full square mile).

When you change a length and want to know the area in different units, remember that area scales with the square of the linear dimension. A square mile equals 640 acres, so convert the smaller square’s area to square miles first, then to acres.

A square half a mile on each side has area (1/2) × (1/2) = 1/4 of a square mile. Convert to acres: 1/4 × 640 = 160 acres. That’s why the amount is 160 acres. The other numbers correspond to different sized areas (for example, 320 acres is half a square mile, and 640 acres is a full square mile).