CalcKit
Trapezoid Calculator
Table of Contents
Trapezoid definition
A trapezoid is a four-sided flat shape (a quadrilateral) with one pair of parallel sides. The two parallel sides are called the bases, and the other two sides are called the legs. Outside North America the same shape is usually called a trapezium.
A trapezoid has the following properties:
- One pair of parallel sides, the two bases, usually of different lengths
- The height is the perpendicular distance between the two bases
- The two angles along each leg add up to 180°
- The line joining the midpoints of the legs (the median, or midsegment) is parallel to the bases, and its length is the average of the two bases
When both pairs of opposite sides are parallel, the shape is a parallelogram. Rectangles, squares and rhombuses are parallelograms too, and under the inclusive definition used by many textbooks, all of them count as trapezoids as well.
Parts of a trapezoid
The four parts of a trapezoid mentioned in this tool are the top base length (a), bottom base length (b), height (h) and area (A). Any three of them give the fourth.
Top base length (a)
The top base is one of the two parallel sides, usually drawn as the shorter one at the top.
If you know the area, the height and the bottom base:
a = 2 * A / h - b
Bottom base length (b)
The bottom base is the other parallel side, usually drawn as the longer one at the bottom.
If you know the area, the height and the top base:
b = 2 * A / h - a
Height (h)
The height of a trapezoid is the perpendicular distance between its two bases. It is not the length of a leg, unless that leg stands at a right angle to the bases.
If you know the area and both bases:
h = 2 * A / (a + b)
Area (A)
The area of a trapezoid is the space enclosed by its four sides. It equals the average of the two bases multiplied by the height:
A = (a + b) / 2 * h
This works because two copies of the same trapezoid, one turned upside down, fit together into a parallelogram with a base of a + b and the same height. The trapezoid is half of it.
Types of trapezoids
Trapezoids are grouped by their legs and angles:
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Isosceles trapezoid: the two legs are the same length, so the shape is symmetrical, its base angles are equal in pairs, and its two diagonals are the same length.
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Right trapezoid: one leg stands at a right angle to both bases, so it has two right angles, and that leg is the height.
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Scalene trapezoid: the legs are of different lengths and none of the angles are equal.
The area formula is the same for all of them, since it only needs the two bases and the height.
Frequently asked questions
How do you find the area of a trapezoid?
Add the two bases, divide by two and multiply by the height: A = (a + b) / 2 * h. For a = 4, b = 10 and h = 5, the area is (4 + 10) / 2 × 5 = 35 square units.
How do you find the height of a trapezoid?
From the area and the two bases: h = 2 * A / (a + b). A trapezoid with A = 35, a = 4 and b = 10 has a height of 2 × 35 / (4 + 10) = 5.
What is the difference between a trapezoid and a trapezium?
They are the same shape under two names. In American English it is a trapezoid, and in British English a trapezium. To add to the confusion, in older American usage a trapezium meant a quadrilateral with no parallel sides.
Is a parallelogram a trapezoid?
It depends on the definition. Under the exclusive definition, a trapezoid has exactly one pair of parallel sides, so a parallelogram is not one. Under the inclusive definition, which many mathematicians prefer, a trapezoid has at least one pair, so every parallelogram is also a trapezoid.