Trapezoid Calculator
Calculate the area, perimeter, and midsegment of a trapezoid using parallel bases and height.
Trapezoid Dimensions
Results:
Area: 0.00 square units
Perimeter: 0.00 units
Midsegment: 0.00 units
Step-by-Step Solution:
About Trapezoids
What is a Trapezoid?
A trapezoid (trapezium in British English) is a quadrilateral with exactly one pair of parallel sides called bases. The non-parallel sides are called legs.
Key Properties
- Has one pair of parallel sides (bases)
- The midsegment is parallel to the bases and equals their average
- The height is perpendicular to both bases
- Sum of interior angles is 360°
- Adjacent angles between base and leg are supplementary
Formulas
Area: A = ½(a + b)h
Perimeter: P = a + b + c + d
Midsegment: m = (a + b)/2
Real-World Applications
- Architecture: Roof trusses, bridge supports
- Furniture: Table legs, chair backs
- Engineering: Dam cross-sections, channel designs
- Design: Handbag shapes, decorative elements
Frequently Asked Questions
What's the difference between a trapezoid and a trapezium?
In American English, a trapezoid has one pair of parallel sides. In British English, this is called a trapezium. The terms are reversed in British English where trapezoid means no parallel sides.
What is the midsegment of a trapezoid?
The midsegment is the line connecting the midpoints of the legs. It's parallel to the bases and its length equals the average of the two bases: (a + b)/2.
Can a trapezoid have right angles?
Yes! A right trapezoid has two right angles adjacent to one leg. This makes calculations easier as the leg with right angles is equal to the height.
How do I find the height if I only know the sides?
You need at least one additional measurement (angle or diagonal). With an angle, use trigonometry. With both diagonals, you can set up equations to solve for height.
Is a parallelogram a trapezoid?
This depends on the definition. Some definitions allow trapezoids to have both pairs of sides parallel (inclusive), while others require exactly one pair (exclusive). In the exclusive definition, a parallelogram is not a trapezoid.
What's an isosceles trapezoid?
An isosceles trapezoid has equal legs (non-parallel sides). It has line symmetry, equal base angles, and equal diagonals. See our Isosceles Trapezoid Calculator for more details.