Trapezium Calculator (Area & Perimeter with Steps)
Calculate the various properties of Trapezium for given values.
Calculator
A Trapezium is a quadrilateral with one pair of parallel sides.
Both UK and US definitions of trapezoid and trapezium are swapped over.
The trapezium is called a trapezoid in the UK.
Formulas
Area :[ ½×(sum of parallel sides)×(distance between them) ] Perimeter:[ (sum of all four sides) ]What is a Trapezium?
A trapezium is a four-sided polygon (quadrilateral) that contains one pair of parallel sides. In many countries, including the United Kingdom, this shape is called a trapezoid. The parallel sides are known as the bases, while the perpendicular distance between them is called the height.
Trapeziums are commonly used in geometry, architecture, engineering, land measurement, bridge design, and construction projects. Understanding how to calculate their area and perimeter helps solve many practical measurement problems.
Area of a Trapezium Formula
The area of a trapezium is equal to half the sum of the parallel sides multiplied by the distance between them.
Area = ½ × (a + b) × h
- a = Length of first parallel side
- b = Length of second parallel side
- h = Distance between the parallel sides
The result is expressed in square units such as cm², m², ft², or in².
Perimeter of a Trapezium Formula
The perimeter of a trapezium is the total distance around its boundary.
Perimeter = a + b + c + d
Where a, b, c, and d represent the lengths of all four sides.
Trapezium Area Examples
| Base 1 | Base 2 | Height | Area |
|---|---|---|---|
| 8 | 12 | 5 | 50 |
| 10 | 14 | 6 | 72 |
| 15 | 20 | 8 | 140 |
Example Calculation
Suppose a trapezium has parallel sides measuring 8 units and 12 units, and the height is 5 units.
Area = ½ × (8 + 12) × 5
Area = ½ × 20 × 5
Area = 50 square units
If the remaining sides are 6 units and 7 units:
Perimeter = 8 + 12 + 6 + 7 = 33 units
Applications of Trapeziums
- Road and bridge engineering
- Roof and building design
- Surveying and land measurement
- Mechanical engineering drawings
- Computer graphics and geometric modelling
- Construction planning
Frequently Asked Questions
What is a trapezium?
A trapezium is a quadrilateral with one pair of parallel sides.
What is the formula for the area of a trapezium?
Area = ½ × (sum of parallel sides) × height.
How do you find the perimeter of a trapezium?
Add the lengths of all four sides.
Can a trapezium have equal non-parallel sides?
Yes. Such a trapezium is called an isosceles trapezium.
What units are used for area?
Area is measured in square units such as cm², m², ft², and in².
What units are used for perimeter?
Perimeter is measured in linear units such as cm, m, ft, and in.