Land area and price math
Land math on the exam comes down to a few facts and three formulas.
Facts to memorize
| Fact | Value |
|---|---|
| 1 acre | 43,560 square feet |
| 1 mile | 5,280 feet |
| 1 section | 1 square mile = 640 acres |
| 1 township | 6 miles square = 36 sections |
| 1 chain | 66 feet (80 chains = 1 mile) |
| 1 rod | 16.5 feet |
All of these come from NIST's tables of U.S. units of measurement.
Area formulas
| Shape | Formula |
|---|---|
| Rectangle or square | Length x Width |
| Triangle | 1/2 x Base x Height |
| Irregular shape | Break it into rectangles and triangles, find each area, then add |
Keep the units consistent. If one side is in yards, convert it to feet before you multiply (1 yard = 3 feet, so 1 square yard = 9 square feet).
Example: triangle. A triangular parcel has a base of 660 feet and a height of 330 feet. 1/2 x 660 x 330 = 108,900 square feet.
Square feet to acres
Divide square feet by 43,560.
108,900 / 43,560 = 2.5 acres.
Going the other way, multiply acres by 43,560. A 40-acre quarter-quarter section is 40 x 43,560 = 1,742,400 square feet.
Price per acre and per square foot
- Total price = acres x price per acre.
- Price per acre = total price / acres.
- The same pattern works for square feet.
Example. The 2.5-acre triangle above sells at $12,000 per acre: 2.5 x 12,000 = $30,000.
Example from a section description. The NW 1/4 of the NE 1/4 of a section is 640 / 16 = 40 acres. At $8,500 per acre, the price is 40 x 8,500 = $340,000.
Price per front foot
Front feet are the feet of a lot's boundary along the street (or water). Read the question carefully to see which dimension is the frontage.
- Price per front foot = total price / front feet.
- Total price = front feet x price per front foot.
Example. A lot is 75 feet wide on the street and 150 feet deep and sells for $120,000. $120,000 / 75 = $1,600 per front foot. The depth does not enter the calculation.
A method that avoids mistakes
- Write down what the question asks for and in what unit.
- Draw the parcel. Split odd shapes into rectangles and triangles.
- Find the area in square feet.
- Convert to acres only if needed (divide by 43,560).
- Apply the price, and check that the answer is a sensible size.
Exam tips
- 43,560 and 5,280 are the two numbers you must know cold.
- Triangle area is half of base times height.
- Front-foot prices ignore depth.