Buildings and lots are rarely rectangles. Almost every measurement problem in appraisal comes down to the same move — cut an awkward outline into pieces you already know how to measure, then add them up. Everything here is geometry in the service of that.
| Shape | Area | Where it shows up |
|---|---|---|
| Rectangle | length × width | Most footprints, most platted lots |
| Triangle | ½ × base × height | Corner lots, angled rear lines, gable ends |
| Trapezoid | ½ × (a + b) × height | Lots whose front and rear widths differ |
| Circle | π × radius2 | Tanks, silos, grain bins, cul-de-sac frontage |
The triangle formula is the one people distrust, so it is worth seeing why the half is there. Any triangle is exactly half of the rectangle that boxes it in — same base, same height. That is the entire derivation.
| Given | To get | Do this |
|---|---|---|
| Square feet | Acres | ÷ 43,560 |
| Acres | Square feet | × 43,560 |
| Square feet | Square yards | ÷ 9 |
| A quarter section | Acres | 640 ÷ 4 = 160 |
That last point is the most useful thing on this page. If two decompositions disagree, one of them has a dimension wrong — which makes working it a second way the cheapest error check available to you. It costs a minute and catches the mistakes that survive careful arithmetic.
Notice that two edges are marked with a ?. Real sketches rarely label everything, and deriving the missing runs from the ones you have is part of the job. Work them out, then find the total area in square feet.
Opposite sides of a closed outline must reconcile. On the sketch above, the two horizontal runs across the top have to add up to the full width along the bottom, and the two vertical runs on the right have to add up to the full height on the left. If they do not, the sketch is wrong or a dimension was misread, and no amount of careful multiplication will rescue it.
A lot 90 feet across the front, 70 feet across the rear, and 150 feet deep is a trapezoid. Its area is half the sum of the parallel sides times the depth:
| Counts as | Rule |
|---|---|
| Gross living area | Finished, above-grade, measured to the exterior walls |
| Reported separately | Below-grade space, however well finished |
| Not living area | Garages, unfinished attics, open porches, decks |
| Site area | The whole legal parcel, before any usability judgement |
Below-grade is the one that causes arguments. A walk-out basement with drywall, carpet and a bathroom is still below grade, and folding it into gross living area overstates the figure every comparable will be measured against. Report it separately and let the adjustment carry its value.