New Jersey Real Estate Salesperson · Real Estate Calculations
Area and Volume
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In 30 seconds
Area is flat space measured in square feet, and volume is filled space measured in cubic feet. The tested distinction is that a rectangle uses length times width, but a triangle uses only half of base times height, and one acre always equals 43,560 square feet.
Why this matters
Area problems are free exam points for anyone who remembers three formulas and the acre conversion, and they are lost by people who multiply the wrong dimensions or forget to halve a triangle.
The college version
In normal terms
- Area of a rectangle is length multiplied by width; area of a triangle is one-half of base multiplied by height; both answers come out in square feet.
- Volume adds the third dimension: length times width times height, answered in cubic feet.
- Convert square feet to acres by dividing by 43,560; convert acres to square feet by multiplying by 43,560.
Concepts in this outline
- Square feet: Length × Width — area of a rectangle, where length is the long side and width is the short side, both measured in feet, giving square feet.
- Area of a triangle: 1/2 × Base × Height — base is any one side and height is the straight-line distance from that side to the opposite corner; multiply, then take half.
- Acres: 1 acre = 43,560 square feet — the fixed conversion between land area and acres; divide square feet by 43,560 to find acres, multiply acres by 43,560 for square feet.
- Cubic feet: Length × Width × Height — volume of a box-shaped space, where height is the vertical dimension; used for basements, warehouses, and fill, answered in cubic feet.
Eli explains
The same idea, in plain words
Explain it like I’m 10
Think of a lot as a sheet of paper on the ground. How much paper there is, measured flat, is its area. For a rectangle you multiply length by width, and the answer is in square feet, because you are counting one-foot squares.
A triangle is a rectangle cut in half along the diagonal, so its area is half of base times height. The most common exam mistake is forgetting that half.
Land is usually sold by the acre, and the conversion never changes: one acre is 43,560 square feet. Divide square feet by 43,560 to get acres, or multiply acres by 43,560 to get square feet.
Volume measures filled space, not flat space. Multiply length, width, and height, and the answer comes out in cubic feet. Volume appears when a problem asks about a basement, a warehouse, or fill dirt.
For an odd-shaped lot, break it into rectangles and triangles, find each piece, and add them. Check that every dimension is in feet before multiplying, because mixing feet and yards gives a wrong answer that looks reasonable.
Worked example
Priya is listing a lot in Paramus for the Okafor family. The main lot is a rectangle 150 feet wide and 200 feet deep, so its area is 150 × 200 = 30,000 square feet. A triangular strip at the back has a base of 40 feet and a height of 30 feet, so it adds 1/2 × 40 × 30 = 600 square feet. The total is 30,600 square feet, and 30,600 ÷ 43,560 = 0.70 acres, rounded, which is what Priya writes in the listing remarks. The buyer also asks about the basement of the existing house, which is 30 feet by 40 feet with an 8-foot ceiling, so its volume is 30 × 40 × 8 = 9,600 cubic feet.
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