Trapezoid Area Calculator
Press Calculate to see the area, the working and other units.
Find the area of any trapezoid from its two parallel sides and its height, or from its midline and height. It works for right, isosceles and scalene trapezoids alike.
A trapezoid has one pair of parallel sides. In British English the same shape is called a trapezium, so a search for either word leads to the same formula. You will find it in tapered garden beds, retaining walls, roof sections and any plot of land with two parallel boundaries of different lengths.
Formula
A = ½ × (b₁ + b₂) × h
- A
- the area
- b₁, b₂
- the two parallel sides, called the bases
- h
- the height, measured at right angles between the bases
Area from the bases and height
Add the two parallel sides, halve the total to get their average, and multiply by the height. A shape with bases of 8 and 14 and a height of 5 covers ½ × (8 + 14) × 5 = 55. The formula works because two copies of a trapezoid, one flipped, fit together into a parallelogram with a base of b₁ + b₂.
Area from the midline and height
The midline joins the midpoints of the two slanted sides, and its length always equals the average of the bases. That makes the area simply midline times height. It is handy for an irregular strip of ground, where the width halfway along is easy to measure. A midline of 11 with a height of 5 gives 55, matching the example above.
- m = (b₁ + b₂) ÷ 2
- A = m × h
Right, isosceles and scalene trapezoids
The area formula is identical for all three. A right trapezoid has one slanted side and one side at 90° to the bases, and that upright side is itself the height. An isosceles trapezoid has slanted sides of equal length. A scalene, or irregular, trapezoid has slanted sides of different lengths and angles.
The slanted sides do not appear in the formula at all. What matters is the perpendicular height, so measure straight across between the bases rather than along a slope. A slanted side is always longer than the height, and using it overstates the area.
Measuring a lot or a yard
For a lot with parallel front and back boundaries, take the two boundary lengths and the perpendicular depth between them. A lot with a 60 ft frontage, a 90 ft rear and a 100 ft depth covers ½ × (60 + 90) × 100 = 7,500 ft², a little over a sixth of an acre. If no two sides are parallel, the shape is not a trapezoid, so use the 4 sides area calculator instead.
Frequently asked questions
What is the formula for the area of a trapezoid?
A = ½ × (b₁ + b₂) × h, where b₁ and b₂ are the parallel sides and h is the perpendicular distance between them.
Is a trapezoid the same as a trapezium?
In American English, a trapezoid has one pair of parallel sides. In British English, that same shape is called a trapezium. The area formula does not change.
How do I find the area of an irregular trapezoid?
Use the same formula. Unequal slanted sides don't affect the area, as long as you measure the height straight across between the two parallel sides.
How do I find the height if I know the area?
Rearrange the formula: h = 2 × A ÷ (b₁ + b₂). An area of 55 with bases of 8 and 14 gives a height of 110 ÷ 22 = 5.
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