Calculate Trapezoid Area
Enter the known measurements and choose what you want to calculate. Use the perpendicular height between the parallel bases, not a sloping side.
Trapezoid diagram
The diagram updates with the entered bases and height. It is illustrative and does not replace a scaled technical drawing.
Trapezoid Area Formula
A trapezoid is a four-sided shape with a pair of parallel sides. The parallel sides are called the bases. The other two sides are called the legs.
Where:
- A is the area.
- a is the length of the first parallel base.
- b is the length of the second parallel base.
- h is the perpendicular distance between the bases.
The formula works by adding the two bases, dividing by two to find their average, and multiplying that average by the height.
Find the missing height
Use this formula when the area and both parallel bases are known.
Find a missing base
Rearrange the area formula when the area, height, and other base are known. The missing base must be positive for a non-degenerate trapezoid.
Find the median or midsegment
The median joins the midpoints of the legs and is parallel to both bases. The area can also be written as A = m × h.
Calculate the perimeter
Here, c and d are the lengths of the two legs. The perimeter cannot generally be determined from the bases and height alone.
Further reading: Math Open Reference: Area of a trapezoid and LibreTexts: The area of a trapezoid.
Worked Trapezoid Area Examples
Example 1: Find the area
A trapezoid has bases of 8 cm and 12 cm and a perpendicular height of 6 cm.
Example 2: Find the height
The area is 60 m² and the bases are 8 m and 12 m.
Example 3: Find a missing base
The area is 60 m², the height is 6 m, and one base is 8 m.
Example 4: Calculate the perimeter
If the bases are 8 cm and 12 cm and the legs are 5 cm and 7 cm:
Example 5: Calculate the median
For bases of 8 m and 12 m, the median is the average of the bases:
If the height is 6 m, the area is also 10 × 6 = 60 m².
Types of Trapezoids
General trapezoid
A general trapezoid has one pair of parallel bases and two legs that may have different lengths and angles. Its area depends on the bases and perpendicular height.
Isosceles trapezoid
An isosceles trapezoid has equal-length legs. Its base angles are equal in pairs, and it has a line of symmetry perpendicular to the bases. The usual trapezoid area formula still applies.
Right trapezoid
A right trapezoid has a leg perpendicular to the bases. That leg is also the height. The other leg may be sloping.
Trapezoid and trapezium terminology
In US usage, a trapezoid is commonly defined as a quadrilateral with at least one pair of parallel sides, though some definitions require exactly one pair. In UK usage, a shape with a pair of parallel sides is commonly called a trapezium. Terminology varies by region, but the area formula remains the same for the shape described on this page.
Frequently Asked Questions
What is the formula for the area of a trapezoid?
The formula is A = (a + b)h / 2. Add the lengths of the two parallel bases, multiply by the perpendicular height, and divide by two.
How do you find the height of a trapezoid?
If the area and both bases are known, use h = 2A / (a + b). The resulting height is the perpendicular distance between the parallel sides.
How do you find a missing base?
Use b = 2A / h − a when the area, height, and other base are known. A valid trapezoid with positive area requires a positive missing base.
Is the sloping side the height?
Usually not. The height is the perpendicular distance between the bases. A sloping leg is only the height when it is perpendicular to the bases, as in a right trapezoid.
How do you calculate the perimeter?
Add all four side lengths: P = a + b + c + d. You need the lengths of both legs as well as the bases. Bases and height alone are not generally enough to find the perimeter.
What is the median of a trapezoid?
The median or midsegment joins the midpoints of the legs. Its length is (a + b) / 2. Multiplying the median by the height gives the area.
Can a trapezoid have equal bases?
If both bases are equal and parallel, the resulting quadrilateral is a parallelogram. Some definitions include parallelograms as trapezoids because they have at least one pair of parallel sides; others reserve the term for exactly one pair.
Does this calculator work with inches and feet?
Yes. Choose millimeters, centimeters, meters, kilometers, inches, feet, or yards. Enter all dimensions in the selected unit, and the area will be returned in that unit squared.