Legal description math: acreage and distances

Separate area from distance

An acre measures area; a foot or mile measures distance. Use 43,560 square feet per acre and 5,280 feet per mile. A standard section is one mile square and contains 640 acres. These are the standard exam assumptions; actual surveyed parcels can differ.

Work through fractional descriptions

Start with the section and work from right to left. The northeast quarter of the southwest quarter means first select the southwest quarter, then its northeast quarter. Multiply 640 by one fourth by one fourth: 640 ÷ 4 = 160, then 160 ÷ 4 = 40 acres. A half of that parcel contains 40 ÷ 2 = 20 acres. Directions locate the parcel; fractions determine its area. Separate, nonoverlapping parcels joined by 'and' are added, while an expressly excluded acreage is subtracted.

Find dimensions and area

A square quarter-section has sides of 5,280 ÷ 2 = 2,640 feet. Its area is 2,640 × 2,640 = 6,969,600 square feet; dividing by 43,560 gives 160 acres. A quarter of the area has half the side length of the original square, not one fourth. By contrast, the east half of a standard section is a rectangle 2,640 feet east to west and 5,280 feet north to south.

For any rectangle, multiply length by width, using matching units, then divide square feet by 43,560 for acres. A 330-foot by 660-foot rectangle contains 330 × 660 = 217,800 square feet; 217,800 ÷ 43,560 = 5 acres. Reverse the conversion by multiplying acres by 43,560. For a triangle, area is one half times base times perpendicular height. Divide an irregular outline into known shapes and add or subtract their areas.

Check what is requested

Perimeter is distance around the boundary: twice length plus twice width for a rectangle. Area alone does not determine frontage or side lengths unless the shape or another dimension is given. Convert miles to feet by multiplying by 5,280; convert feet to miles by dividing. Keep intermediate values exact and round only the final result as requested.