Trapezoid Area Calculator
Find the area of a trapezoid from its bases and height.
Results update as you type.
How it works
A trapezoid, called a trapezium in British English, is a four-sided shape with exactly one pair of parallel sides, known as the bases. Roof cross-sections, table tops, bridge supports, and many plots of land take this form, so calculating a trapezoid's area is a common practical need. This trapezoid area calculator takes three inputs, the lengths of the two parallel bases and the perpendicular height between them, and returns the area, the flat space the shape covers. The formula averages the two bases and multiplies by the height: you add the two parallel sides, divide by two to get their average width, then multiply by the distance separating them. This is the same as finding the area of a rectangle whose width equals the average of the two bases. For a trapezoid with bases of 4 and 6 units and a height of 3 units, the average base is 5 units, so the area is 5 times 3, which is 15 square units. Students learning geometry, builders estimating roofing or decking, and surveyors measuring irregular plots all rely on a trapezoid area calculator to handle the averaging step cleanly and avoid using the slanted sides by mistake.
area = (base₁ + base₂) ÷ 2 × height
The area of a trapezoid is the average of the two parallel sides multiplied by the distance between them. Averaging the bases works because the shape widens or narrows evenly from one parallel side to the other, so the mean of the two lengths represents its typical width. Multiplying that average width by the perpendicular height gives the enclosed area, exactly as multiplying width by height gives the area of the equivalent rectangle.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base 1 (a), base 2 (b) and height (h).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Area updates instantly as you type — no button to press.
Frequently asked questions
What is the formula for the area of a trapezoid?
The area of a trapezoid is the sum of the two parallel bases divided by two, multiplied by the height. Written out, it is one half times base one plus base two, times the height. The height must be the perpendicular distance between the parallel sides. For bases of 4 and 6 with a height of 3, the area is one half times 10 times 3, which equals 15 square units.
Which sides are the bases?
The bases are the two sides that are parallel to each other. A trapezoid has exactly one pair of parallel sides, and those two are the bases used in the formula. The other two sides, called the legs, can be slanted and of any length, and they are not used to calculate the area. Identifying the parallel pair correctly is the key step before applying the formula.
What height should I use?
Use the perpendicular height, the shortest straight-line distance between the two parallel bases, measured at a right angle to them. Do not use the length of the slanted legs, which is longer and would overstate the area. If a trapezoid is drawn tilted, the height is still measured straight across between the parallel sides, not along the sloping edge. The calculator assumes you enter this perpendicular height.
Why does averaging the bases work?
Because a trapezoid changes width evenly from one base to the other, the average of the two base lengths represents its effective width across the middle. Multiplying that average width by the height gives the same area as an equal-height rectangle of that average width. You can also picture two copies of the trapezoid joined to form a parallelogram, whose area is the base sum times height, then halved.
Does the order of the two bases matter?
No. Because the formula adds the two bases together before dividing, it does not matter which one you label as base one and which as base two. Addition gives the same total either way, so the area comes out identical regardless of the order you enter them. Just make sure both values are the parallel sides and that the height is the perpendicular distance between them.