Trapezoid Square Footage Calculator
For rooms, yards, or roof planes with two parallel sides of different length. Formula: ((a + b) / 2) × h.
Last updated:Tip: If you only have the diameter, divide by 2 to get the radius.
L-shape = two rectangles sharing a corner.
Add one row per rectangle and we'll sum them.
Trapezoid Area Formula
A trapezoid has one pair of parallel sides. The area is the average of the two parallel sides multiplied by the perpendicular distance between them: Area = ((a + b) / 2) × h.
- a = 8 ft, b = 14 ft, h = 6 ft → ((8 + 14) / 2) × 6 = 66 sq ft
- a = 20 ft, b = 30 ft, h = 12 ft → ((20 + 30) / 2) × 12 = 300 sq ft
- a = 10 ft, b = 16 ft, h = 30 ft (a tapered driveway) → ((10 + 16) / 2) × 30 = 390 sq ft
The Midsegment Reading
(a + b) / 2 is not a random average — it is the midsegment, the segment joining the midpoints of the two non-parallel sides. So the area is simply midsegment × height: an 8 ft × 14 ft trapezoid behaves like a rectangle 11 ft wide (the average of 8 and 14) and h tall. That is a useful sanity check before you trust any answer — if your midsegment times height does not match, an input is wrong.
Worked Example
A room that is 14 ft along the back wall, 8 ft along the front wall, and 6 ft deep:
- Average the parallel sides: (8 + 14) / 2 = 11 ft.
- Multiply by the perpendicular depth: 11 × 6 = 66 sq ft.
- Cross-check by dissection: a central 8 ft × 6 ft rectangle = 48 sq ft, plus two side triangles that together make (14 − 8) × 6 / 2 = 18 sq ft. 48 + 18 = 66 sq ft ✓.
- Unit conversions of the same 66 sq ft: 6.13 m² (66 × 0.09290304), 7.33 sq yd (66 ÷ 9), 9,504 sq in (66 × 144), 0.001515 acre (66 ÷ 43,560).
Why the Dissection Works
Drop two perpendiculars from the short side to the long side. You get a rectangle of a × h and two triangles whose bases sum to b − a, so their combined area is (b − a) × h / 2. Add them:
a × h + (b − a) × h / 2 = h × (a + b) / 2
The formula is not a rule to memorise; it is the rectangle-plus-triangles result simplified. It also means the split does not have to be symmetric — an off-center (scalene) trapezoid gives the same sum because only the total of the two triangle bases matters.
The Slant-Side Trap
The h in the formula is the perpendicular distance between the parallel sides, never the slanted side. In the 8 ft / 14 ft / 6 ft room above, each side runs out (14 − 8) / 2 = 3 ft horizontally, so the slanted wall is √(6² + 3²) = 6.71 ft. Enter 6.71 as the height and you get (8 + 14) / 2 × 6.71 = 73.79 sq ft — 11.8% more than the truth, which is about 8 sq ft of flooring you did not need.
If you measured the slant and the angle instead, convert first: h = slant × sin(θ), where θ is the angle the slant makes with the base. With a 60° rake and a 6.71 ft slant, h = 6.71 × sin 60° = 5.81 ft.
Solving Backwards
Two rearrangements come up constantly on jobs:
- Height from area:
h = 2 × Area / (a + b). To get 66 sq ft between parallel widths of 8 ft and 14 ft, the run must be 2 × 66 / 22 = 6 ft. - Base from area:
a = 2 × Area / h − b. With 66 sq ft, h = 6 ft and b = 14 ft, the other side is 2 × 66 / 6 − 14 = 22 − 14 = 8 ft.
The widget above does not solve backwards — it takes dimensions and returns area — so write the rearrangement on your sketch and check the entered numbers against it.
Types of Trapezoid
| Type | Defining property | Area formula |
|---|---|---|
| Scalene | No equal sides, no right angles | ((a + b) / 2) × h |
| Isosceles | The two non-parallel sides are equal | ((a + b) / 2) × h |
| Right | Two right angles; one leg is the height | ((a + b) / 2) × h |
Type changes the perimeter and the slant lengths, never the area — which is why a "tapered" side yard and a "skewed" one with the same two bases and the same perpendicular width hold the same number of square feet.
Trapezoid or Parallelogram? Two Definitions
US school textbooks usually define a trapezoid as having exactly one pair of parallel sides, which keeps parallelograms outside the club. Most mathematicians use the inclusive definition — at least one pair — which makes every parallelogram, rectangle, and square a trapezoid. Both conventions are in everyday use, and here they do not conflict: put a = b in ((a + b) / 2) × h and it collapses to a × h, the rectangle formula. So the tab on this page is safe for a rectangular room too; enter the same number in both side fields.
Common Uses
Trapezoidal shapes are common in real-world settings: side yards of homes, certain roof planes, irregular garden beds, and driveway entries that taper. A tapered driveway (10 ft wide at the street, 16 ft wide at the garage, 30 ft long) has an area of ((10 + 16) / 2) × 30 = 390 sq ft. At 0.15 cu yd of asphalt per 100 sq ft installed, order by volume from the supplier's cover rate — area alone does not price the job.
For a room that tapers on both walls at once — a bump-out with angled returns — the shape is still a trapezoid as long as the two ends stay parallel. If the ends are not parallel, split it with the irregular calculator.
FAQ
How do I calculate square footage of a trapezoid?
Average the two parallel sides, then multiply by the perpendicular distance between them: Area = ((a + b) / 2) × h. For a = 8 ft, b = 14 ft, h = 6 ft: (8 + 14) / 2 = 11 ft, then 11 × 6 = 66 sq ft. Those three numbers are the whole input — the slant lengths do not enter the area at all.
What is the midsegment of a trapezoid and why does it matter?
The midsegment joins the midpoints of the two non-parallel sides and its length is m = (a + b) / 2. The area is then m × h, which says something useful: a trapezoid holds the same area as a rectangle as wide as the average of its bases. For 8 ft and 14 ft, m = 11 ft, so the 6 ft-deep room is an 11 × 6 = 66 sq ft rectangle in disguise.
Can I use the slanted side instead of the height?
No — that is the classic trapezoid mistake. With a = 8, b = 14 and a 6 ft vertical drop, each side runs out 3 ft, so the slant is √(6² + 3²) = 6.71 ft. Using 6.71 as the height gives 11 × 6.71 = 73.79 sq ft instead of 66 sq ft, an 11.8% overshoot. Convert first with h = slant × sin(θ), or measure straight down with a story pole.
How do I find the height when I know the area?
Rearrange: h = 2 × Area / (a + b). To cover 66 sq ft between parallel widths of 8 ft and 14 ft, the run is 2 × 66 / 22 = 6 ft. Likewise a = 2 × Area / h − b recovers a base. The calculator on this page runs one direction only — dimensions in, area out — so do the rearrangement on paper.
What is the difference between a trapezoid and a parallelogram?
It depends on which convention your textbook uses. The exclusive definition says a trapezoid has exactly one pair of parallel sides, so a parallelogram (two pairs) is not a trapezoid. The inclusive definition says at least one pair, so a parallelogram is a special trapezoid. Neither choice breaks the arithmetic: with a = b the formula becomes a × h, the parallelogram area.
Do the different types of trapezoid need different formulas?
No. Scalene (no equal sides), isosceles (equal legs) and right (two right angles) trapezoids all take ((a + b) / 2) × h, because the formula uses only the two parallel sides and the perpendicular distance. A right trapezoid is the easiest to measure on site: one wall is already the height.
Does this calculator give me the perimeter too?
No. Area only. A trapezoid's perimeter needs all four sides, and the legs cannot be recovered from a, b and h — shear the same 8/14/6 trapezoid sideways and the legs change length while the area stays 66 sq ft. If you need fencing, skirting, or trim, measure the slant runs directly; see square feet to linear feet for the area-to-length conversion.
What units should I enter?
Each field has its own unit dropdown (ft, in, yd, m, cm) and the tool converts to feet before applying the formula, so side a can be in feet while the height is in inches. Results appear in square feet plus square meters, square yards, acres and square inches. The underlying length definition is exact: 1 ft = 0.3048 m.
Sources and How to Check This Page
- The length and area units come from NIST Special Publication 811, Appendix B.9.1: 1 ft = 0.3048 m exactly and 1 sq ft = 9.290 304 E−02 m². Every conversion on this page is arithmetic on that exact factor, not a measured ratio.
- The exact-foot definition and the retirement of the US survey foot are in 85 FR 62698, which fixes the international foot at 0.3048 m and deprecates the survey foot as of December 31, 2022.
- The formula needs no external authority — re-derive it in two minutes: a rectangle a × h plus two triangles summing to (b − a) × h / 2 gives h × (a + b) / 2. Check the numbers on this page with that: 8 × 6 = 48, (14 − 8) × 6 / 2 = 18, 48 + 18 = 66.
- The slant-side error is pure Pythagoras and reproducible: √(6² + 3²) = 6.7082, 11 × 6.7082 = 73.79, 73.79 ÷ 66 − 1 = 11.8%.
- What this page does not claim: perimeter, leg lengths, or angles from three inputs. Those are underdetermined — many trapezoids share one pair of bases and one height. If your shape has no parallel sides at all, use the property size calculator for four-sided lots instead of forcing it through this formula.