Trapezoid Calculator
Calculate area, perimeter, height, median, and diagonals from any known values
Trapezoid Calculator
How to Use the Trapezoid Calculator
- Select Input Method: Choose how you want to define the trapezoid - by bases and height, all four sides, or as an isosceles trapezoid
- Enter Values: Input the known measurements
- View Results: All properties are calculated automatically including area, perimeter, height, median, and diagonals
- Copy Values: Click the copy button next to any result
Understanding Trapezoids
A trapezoid (called trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs.
Key Components:
- Bases (a, b): The two parallel sides
- Legs (c, d): The two non-parallel sides
- Height (h): Perpendicular distance between the bases
- Median (m): Line connecting midpoints of the legs
Types of Trapezoids:
- Isosceles Trapezoid: Both legs are equal length
- Right Trapezoid: Has two right angles
- Scalene Trapezoid: No equal sides
Trapezoid Formulas
Area Formulas
Perimeter & Median
Isosceles Trapezoid
Practical Applications
Architecture & Construction
- Roof sections and gables
- Bridge deck cross-sections
- Retaining wall designs
- Window and door frames
Engineering
- Channel and duct cross-sections
- Hydraulic calculations
- Structural beam profiles
- Foundation footings
Everyday Uses
- Lamp shade dimensions
- Table and desk shapes
- Garden bed layouts
- Fabric cutting patterns
Mathematics & Education
- Numerical integration (trapezoidal rule)
- Area approximation methods
- Geometry curriculum
- Problem-solving exercises
Frequently Asked Questions
How do I find the area of a trapezoid?
The area of a trapezoid is calculated using A = ½(a + b) × h, where a and b are the parallel sides (bases) and h is the perpendicular height between them. You can also use A = m × h, where m is the median.
What is the median of a trapezoid?
The median (or midsegment) is a line segment connecting the midpoints of the two legs. Its length equals the average of the two bases: m = (a + b) / 2. It is parallel to both bases.
How do I calculate the height of an isosceles trapezoid?
For an isosceles trapezoid with parallel sides a and b and leg length c, the height is h = √(c² - ((a-b)/2)²). This uses the Pythagorean theorem on the right triangle formed.
What is the difference between a trapezoid and a trapezium?
In American English, a trapezoid has exactly one pair of parallel sides. In British English, this same shape is called a trapezium. The terminology is reversed between the two conventions.
What are the properties of an isosceles trapezoid?
An isosceles trapezoid has: one pair of parallel sides, equal non-parallel sides (legs), equal base angles, equal diagonals, and a line of symmetry perpendicular to the parallel sides.