Area of a Trapezoid Calculator

What is a trapezoid?

A trapezoid is a four-sided shape with one pair of parallel sides. The two parallel sides are called the bases; the other two sides are the legs and may be of different lengths. The height is the perpendicular distance between the bases, not the length of a slanted leg.

The name varies by region. In North American usage "trapezoid" means exactly one pair of parallel sides, while British usage calls the same figure a "trapezium". Some textbooks allow two pairs, which would make a parallelogram a special trapezoid. The formula below works in every case.

Area of a trapezoid formula

Average the two bases, then multiply by the height.

A = (a + b) ÷ 2 × ha and b are the parallel bases and h is the height measured at right angles to them.

The average (a + b) ÷ 2 is the length of the midsegment, the line that joins the midpoints of the two legs. The trapezoid has the same area as a rectangle whose width is that midsegment and whose height is h.

Why it works: put a second copy of the trapezoid upside down next to the first. The two pieces fit together into a parallelogram with base a + b and height h, whose area is (a + b) × h. One trapezoid is half of that, which gives the formula above.

How to use the calculator

1. Pick the unit you want the answer in from the Metric list.
2. Type the lengths of Base 1 and Base 2, the two parallel sides, in any order.
3. Type the Height, the perpendicular distance between those sides.
4. Press Calculate area. The result shows the area in squared units followed by the unit written out, for instance 0.8750 m² (square meters).

Each of the three measurements has its own unit selector, so you can enter one base in centimetres and the other in metres without converting by hand. The calculator converts every length first and expresses the area in the unit chosen in the Metric box. Set the unit next to each measurement to match what you actually measured; changing the Metric list alone only changes the unit of the answer.

All three values are required and must be zero or larger. Results with a short fractional part are shown with two or four decimals, longer ones with six, and whole numbers without a decimal point.

Worked examples

Example 1: a flower bed. The parallel sides of a bed are 3 m and 5 m long and the distance between them is 2.4 m. Area = (3 + 5) ÷ 2 × 2.4 = 4 × 2.4 = 9.6 m².

Example 2: mixed units. One base is 90 cm, the other 1.5 m and the height 60 cm; you want square metres. Converting gives 0.9 m, 1.5 m and 0.6 m, so the area is (0.9 + 1.5) ÷ 2 × 0.6 = 1.2 × 0.6 = 0.72 m². In the calculator, set each row to its own unit and leave Metric on m.

Example 3: a missing base. A trapezoid has area 54 cm², height 6 cm and one base of 7 cm. Rearranging the formula, b = 2A ÷ h − a = 108 ÷ 6 − 7 = 18 − 7 = 11 cm. Check: (7 + 11) ÷ 2 × 6 = 54.

Example 4: only the legs are known. An isosceles trapezoid has bases 6 and 14 and equal legs of 5. Each leg runs 4 units sideways, because (14 − 6) ÷ 2 = 4, so by the Pythagorean theorem the height is √(5² − 4²) = 3. The area is (6 + 14) ÷ 2 × 3 = 30.

Units and conversions

The calculator accepts millimetres, centimetres, decimetres, metres, kilometres, inches, feet, yards and miles. Internally every length is brought to a common unit, the area is computed, and the answer is expressed in the unit you selected in the Metric box. Area units scale with the square of the length unit: 1 m² is 10,000 cm², and 1 yd² is 9 ft².

If you already have an area in one unit and need another, use the area unit converter. For lengths, the length converter is the faster option.

Common mistakes

• Using a leg as the height. A slanted leg is longer than the true height. Unless the trapezoid is a right trapezoid, work out the perpendicular distance first.
• Adding the bases and forgetting to halve. (a + b) × h is the area of the double trapezoid, which is a parallelogram. Divide by 2.
• Using the non-parallel sides as bases. Only the parallel sides go into Base 1 and Base 2.
• Mixing units silently. A base of 90 and a height of 0.6 mean different things if one is in centimetres and the other in metres. Check every unit selector.

Related shapes

When both bases are equal, the trapezoid is a parallelogram and the formula reduces to base times height; see the area of a parallelogram calculator. Cutting a trapezoid along a diagonal produces two triangles, which you can check with the area of a triangle calculator. For simpler figures there are the rectangle, square and circle versions.