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Trapezoid Area Calculator

The area of a trapezoid is the average of its two parallel sides times the perpendicular height between them: area = ½ × (a + b) × h. Type 4 and 6 for the parallel sides and 6 for the height and the answer is 30, with the working printed underneath as ½ × (4 + 6) × 6 = 30, so you can check the arithmetic yourself. This page opens on the trapezoid rather than the rectangle, with the shape drawn beside the answer and its two parallel sides and its height labelled with the numbers you typed. The slanted sides never enter the formula: a leaning trapezoid and an upright one with the same a, b and h have exactly the same area. All three numbers go in one unit, millimetres, centimetres, metres, inches or feet, the area comes back in that unit squared, and the rows below list the same area in six more units, so a plot measured in feet still reads in square metres.

a = 4 cmb = 6 cmh = 6 cm
Trapezoid · ½ (a + b) h30cm²3,000 mm² · 0.003 m² · 4.65001 in²
Flat
Solid, surface area
Side a (cm)
Side b (cm)
Height (cm)
Unit

a and b are the two parallel sides; the height is the distance between them.

  • The workingarea, in cm²
    ½ × (4 + 6) × 6 = 30
  • Square millimetresmm²
    3,000
  • Square metresm²
    0.003
  • Square inchesin²
    4.65000930002
  • Square feetft²
    0.0322917312501
  • Square yardsyd²
    0.0035879701389
  • Acresac
    7.413161e-7
The formula is on the stage, and the working is the first row. Every answer here is one textbook formula with your numbers put in, printed so you can check it: a circle is π r², a three-sided triangle is Heron's formula, a regular polygon is n s² / (4 tan(π/n)). The solids give surface area for a closed shape, both ends of a cylinder and the base of a cone included. Conversions use exact definitions, so a square foot is 0.09290304 m² and 43,560 of them make an acre.

Common questions

What is the formula for the area of a trapezoid?
Area = ½ (a + b) h, where a and b are the two parallel sides and h is the perpendicular distance between them. The formula sits on the stage beside the answer, and the first row under it is that formula with your numbers in place, for example ½ × (4 + 6) × 6 = 30. Read another way, it is the average of the two parallel sides, (a + b) / 2, multiplied by the height. That average, the midsegment, is not printed as its own figure here.
Which side is a and which is b?
Either way round, because addition does not care. The two fields labelled Side a and Side b are the two parallel sides, drawn as the top and bottom edges of the figure and labelled a and b with your numbers. Height is the third field. Sides of 8 and 12 with a height of 5 give 50, and so do sides of 12 and 8 with the same height.
Do I need the slanted sides, the legs?
No, and there is nowhere to type them: only the two parallel sides and the height between them decide the area. If you know a leg of an isosceles trapezoid but not the height, work the height out by Pythagoras first: h = √(leg² − ((b − a) / 2)²). Parallel sides of 4 and 10 with legs of 5 give h = √(25 − 9) = 4, and typing 4, 10 and 4 here returns 28. That square root is one to do before you get here.
Is this the shape I was taught to call a trapezium?
Probably, yes. In American usage a trapezoid is a quadrilateral with a pair of parallel sides, and that is the shape this page computes; British schools call the same shape a trapezium and use trapezoid for a quadrilateral with no parallel sides at all. A four-sided figure with nothing parallel has no ½ (a + b) h to apply: split it into two triangles along a diagonal and add the two areas with the Triangle shape.
What happens if the two parallel sides are equal?
You get a parallelogram, and the formula still holds: ½ (b + b) h is just b h. Sides of 6 and 6 with a height of 5 print ½ × (6 + 6) × 5 = 30, the same 30 a 6 by 5 rectangle gives on the Rectangle shape. The height is still the straight distance between the parallel sides, not the length of the sloping edge.
Which units can I use, and how is the conversion done?
Type all three numbers in millimetres, centimetres, metres, inches or feet, and the area comes back in that unit squared. A deck with parallel edges of 10 ft and 14 ft standing 8 ft apart is 96 ft², listed in the rows below as 8.91869184 m², 10.6666666667 yd², 13,824 in² and 0.00220385674931 acres. The conversions use exact definitions, so a square foot is exactly 0.09290304 square metres. Feet and inches together go in as a decimal: 8 ft 6 in is 8.5.
Why was my number rejected, and what can I type?
The fields take plain numbers, with decimals and with thousands commas, so 10.5 and 1,200 are both fine while a fraction like 1/2 is not: that one says "Side a needs a number, like 5: "1/2" is not one." An empty field says "Side a is empty: type a number, like 5." A zero or a negative says "Height must be greater than 0." The message sits under the fields and names the field to fix.
Can I work backwards from the area to a missing side?
Not on this page: it goes from the three numbers to the area and never the other way. The rearrangement is one line, though. With the area A, the height h and one parallel side a, the other is b = 2A / h − a, so an area of 30 with a height of 6 and a side of 4 gives 2 × 30 / 6 − 4 = 6. Type that 6 back in to check it.

Every area is computed from the formula shown, exact to the precision of the numbers you type, and conversions use exact unit definitions. Measurements from the real world carry their own error.